{"id":6049,"date":"2025-06-09T17:39:26","date_gmt":"2025-06-09T17:39:26","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=6049"},"modified":"2025-06-09T17:39:26","modified_gmt":"2025-06-09T17:39:26","slug":"rs-aggarwal-quantitative-aptitude-pdf-free-download-charts-pie","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/rs-aggarwal-quantitative-aptitude-pdf-free-download-charts-pie\/","title":{"rendered":"RS Aggarwal Quantitative Aptitude PDF Free Download: PIE-CHARTS"},"content":{"rendered":"

PIE-CHARTS<\/strong><\/h1>\n

IMPORTANT FACTS AND FORMULAE<\/strong><\/h2>\n

The pie-chart<\/strong> or a pie-graph<\/strong> is a method of representing a given numerical data in the form of sectors of a circle.<\/p>\n

The sectors of the circle are constructed in such a way that the area of each sector is proportional to the corresponding value of the component of the data.<\/p>\n

From geometry, we know that the area of a circle is proportional to the central angle.<\/p>\n

So, the central angle of each sector must be proportional to the corresponding value of the component.<\/p>\n

Since the sum of all the central angle is 360\u00b0, we have\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Value of the component \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00b0\u00a0\u00a0<\/p>\n

Central angle of the component =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ———————— * 360\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Total value\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

SOLVED EXAMPLES<\/strong><\/h2>\n

The procedure of solving problems based on pie-charts will be clear from the following solved examples.<\/p>\n

Example 1. The following pie-chart shows the sources of funds to be collected by the National Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answer the questions that follow.<\/em><\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SOURCES OF FUNDS TO BE ARRANGED BY\u00a0 NHAI<\/strong><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 FOR PHASE II PROJECTS (IN CRORES RS.)<\/strong><\/p>\n

\"\"<\/p>\n

Total funds to be arranged for Projects (Phase II) =Rs.57,600 crores.<\/p>\n

    \n
  1. Near about 20% of the funds are to be arranged through:<\/li>\n<\/ol>\n

    (a) SPVS\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) External Assistance<\/p>\n

    (c) Annuity \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) Market Borrowing<\/p>\n

      \n
    1. The central angle corresponding to Market Borrowing is:<\/li>\n<\/ol>\n

      (a) 52\u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 137.8\u00b0<\/p>\n

      (c) 187.2\u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 192.4\u00b0<\/p>\n

        \n
      1. The approximate ratio of the funds to be arranged through Toll and that through Market Borrowing is:<\/li>\n<\/ol>\n

        (a) 2:9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 1:6<\/p>\n

        (c) 3:11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 2:5<\/p>\n

          \n
        1. If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent (approximately) should it increase the Market Borrowings to arrange for the shortage of funds ?<\/li>\n<\/ol>\n

          (a) 4.5%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 7.5%<\/p>\n

          (c) 6%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 8%<\/p>\n

          5.If the toll is to be collected through an outsourced agency by allowing a maximum 10% commission, how much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs. 4910 crores ?<\/p>\n

          (a) Rs.6213 crores\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) Rs. 5827 crores<\/p>\n

          (c) Rs. 5401 crores\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) Rs. 5216 crores<\/p>\n

          SOLUTION<\/strong><\/h2>\n
            \n
          1. (b): 20% of the total funds to be arranged = Rs.(20% of 57600) crores<\/li>\n<\/ol>\n

            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = Rs.11520 crores Rs.11486 crores.<\/p>\n

              \n
            1. (c):Central angle corresponding to Market Borrowing = 29952<\/li>\n<\/ol>\n

              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ——–\u00a0 * 360\u00b0<\/p>\n

              \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 57600<\/p>\n

              \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 187.2\u00b0<\/p>\n

                \n
              1. (b): 4910\u00a0\u00a0\u00a0\u00a0\u00a0 1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1<\/li>\n<\/ol>\n

                \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Required ratio =\u00a0 ——- = —- = —-<\/p>\n

                \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 29952\u00a0\u00a0\u00a0 6.1\u00a0\u00a0\u00a0\u00a0\u00a0 6\u00a0\u00a0<\/p>\n

                  \n
                1. (c):Shortage of funds arranged through External Assistance<\/li>\n<\/ol>\n

                  \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =Rs.(11486-9695) crores =Rs. 1791 crores.<\/p>\n

                  \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 therefore, Increase required in Market Borrowings =Rs. 1791 crores.<\/p>\n

                  \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a01791\u00a0\u00a0\u00a0\u00a0<\/p>\n

                  \u00a0\u00a0\u00a0\u00a0 Percentage increase required =\u00a0\u00a0\u00a0\u00a0 ——– * 100\u00a0\u00a0 % =\u00a0 5.98 % = 6%<\/p>\n

                  \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 29952<\/p>\n

                    \n
                  1. (c):Amount permitted = (Funds required from Toll for projects of Phase II ) +<\/li>\n<\/ol>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (10 % of these funds)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =Rs. 4910 crores + Rs. (10% of 4910) crores\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =Rs. (4910 + 491) crores = Rs. 5401 crores.<\/p>\n

                    Example 2. The pie-chart provided below gives the distribution of land (in a village) under various food crops. Study the pie-chart carefully and answer the questions that follow.<\/em><\/strong><\/p>\n

                    \u00a0\u00a0\u00a0 DISTRIBUTION OF AREAS (IN ACRES) UNDER VARIOUS FOOD CROPS<\/strong><\/h3>\n

                    1.Which combination of three crops contribute to 50% of the total area under the food crops ?<\/p>\n

                    (a) Wheat, Barley and Jowar\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b)Rice, Wheat and Jowar<\/p>\n

                    (c) Rice, Wheat and Barley\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d)Bajra, Maize and Rice\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    2.If the total area under jowar was 1.5 million acres, then what was the area (in million acres) under rice?<\/p>\n

                    (a)6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b)7.5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c)9\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d)4.5<\/p>\n

                    3.If the production of wheat is 6 times that of barley, then what is the ratio between the yield per acre of wheat and barley ?<\/p>\n

                    (a) 3:2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 3:1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 12:1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 2:3<\/p>\n

                    4.If\u00a0 the yield per acre of rice was 50% more than that of barley, then the production of barley is what percent of that of rice ?\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    (a)30%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b)33 %\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c)35%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d)36%<\/p>\n

                    5.If the total area goes up by 5%, and the area under wheat production goes up by 12%\u00a0\u00a0 , then what will be the angle for wheat in the new pie-chart ?<\/p>\n

                    (a) 62.4\u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 76.8\u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 80.6\u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 84.2\u00b0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SOLUTIONS<\/strong><\/h3>\n

                    1.(c):The total of the central angles corresponding to the three crops which cover 50% of the total area ,should be 180\u00b0.Now, the total of the central angles for the given combinations are:<\/p>\n

                    (i)\u00a0\u00a0 Wheat,Barley and jowar = (72\u00b0+36\u00b0+18\u00b0)=126\u00b0<\/p>\n

                    (ii)\u00a0 Rice,Wheat and Jowar = (72\u00b0+72\u00b0+18\u00b0)=162\u00b0<\/p>\n

                    (iii) Rice,Wheat and Barley = (72\u00b0+72\u00b0+36\u00b0)=180\u00b0<\/p>\n

                    (iv)Bajra,Maize and Rice = (18\u00b0+45\u00b0+72\u00b0) = 135\u00b0\u00a0<\/p>\n

                    Clearly:(iii) is the required combination.<\/p>\n

                    2.(a):\u00a0\u00a0 The area under any of the food crops is proportional to the angle corresponding to that crop.<\/p>\n

                    Let the area under the rice production be x million acres.<\/p>\n

                    Then, 18:72 = 1.5:x \u00de x=(72*15\/18)=6<\/p>\n

                    Thus, the area under rice production be = 6 million acres.<\/p>\n

                    3.(b): Let the total production of barley be T tones and let Z acres of land be put under barley\u00a0\u00a0\u00a0 production.<\/p>\n

                    Then, the total production of wheat =(6T) tones.<\/p>\n

                    Also,area under wheat production = (2Z) acres.<\/p>\n

                    \\Area Under Wheat Production\u00a0\u00a0\u00a0\u00a0 72\u00b0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    \u00a0\u00a0 ————————————- = —-\u00a0\u00a0 =2\u00a0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Area Under Barley Production\u00a0\u00a0\u00a0 36\u00b0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 And therefore,Area under wheat = 2*Area under Barley = (2Z)acres<\/p>\n

                    Now, yield per acre for wheat = (6T\/2Z) tones\/acre = (3T\/Z) tones\/acre<\/p>\n

                    And yield per acre for barley = (T\/Z) tones\/acre.<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3T\/Z<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\Required ratio\u00a0 = ——– = 3:1. \u00a0<\/p>\n

                    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 T\/Z<\/p>\n

                      \n
                    1. (b):Let Z acres of land be put under barley production.<\/li>\n<\/ol>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Area Under Rice Production\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 72 \u00b0<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Then,\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ———————————–\u00a0\u00a0 =\u00a0\u00a0 —-\u00a0 =\u00a0 2.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Area Under Barley Production\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 36\u00b0<\/p>\n

                      \\Area under rice production = 2 * area under barley production = (2Z) acres.<\/p>\n

                      Now,if p tones be the yield per acre of barley then ,yield per acre of rice<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =(p+50% of p) tones =(3\/2 p) tones.<\/p>\n

                      \\Total production of rice = (yield per acre) * (area under production)<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0 (3\/2 p)*2Z=(3pZ) tones.<\/p>\n

                      And,Total production of barley = (pz) tones.<\/p>\n

                      \\Percentage production of barley to that rice = (pZ\/3pZ *100)%= 33 1\/3% .<\/p>\n

                      5.(b): Initially,let\u00a0 t\u00a0 be the total area under considerations.<\/p>\n

                      The area under wheat production initially was =(72\/360 * t)acres\u00a0 =\u00a0 (t\/5)acres.<\/p>\n

                      Now,if the total area under consideration be increased by 5%,<\/p>\n

                      then the new value of the total area= (105\/100 t) acres.<\/p>\n

                      Also,if the area under wheat production be increased by 12%,<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0t<\/p>\n

                      then the new value of area under wheat =\u00a0\u00a0\u00a0\u00a0 —\u00a0 +(12% of\u00a0\u00a0 –)\u00a0\u00a0 acres = (112t\/500)acres.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5<\/p>\n

                      \u00a0\\Central angle corresponding to wheat in the pie-chart<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Area\u00a0 Under Wheat (new)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00b0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (112t\/500)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00b0<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 ——————————- *360\u00a0\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0 ————*<\/strong>360\u00a0\u00a0\u00a0\u00a0\u00a0 =76.8\u00b0<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Total area (new) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(105t\/100)<\/p>\n

                      Example 3.The following pie-charts show the distribution of students of graduate and post graduate levels in seven different institute-M,N,P,Q,R,S and T in a town.<\/em><\/strong><\/p>\n

                      DISTRIBUTION OF STUDENTS AT GRADUATE AND POST-GRADUATE\u00a0\u00a0\u00a0\u00a0 LEVELS\u00a0 IN SEVEN INSTITUTES-M,N,P,Q,R,S AND T.<\/strong><\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Total\u00a0\u00a0\u00a0\u00a0 Number of students of\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Total\u00a0\u00a0\u00a0\u00a0 Number of students of\u00a0\u00a0 <\/strong><\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0graduate level\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 post graduate level<\/strong><\/p>\n

                      1.How many students of institutes M and S are studying at graduate level?<\/p>\n

                      \u00a0\u00a0\u00a0 (a) 7516\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 8463\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 9127\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 9404<\/p>\n

                      2.Total number of students studying at post -graduate level from institutes N and P is:<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0 (a) 5601\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 5944\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 6669\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 7004<\/p>\n

                      3.What is the total number of graduate and post-graduate level students in institute R?<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0 (a) 8320\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 7916\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 9116\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 8372<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0 4 .What is the ratio between the number of students studying at post graduate and graduate levels\u00a0\u00a0\u00a0 respectively from institute S?<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (a) 14:19\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 19:21\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 17:21\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 19:14<\/p>\n

                      5.What is the ratio between the number of students studying post graduate level from institute S\u00a0 and the number of students studying at graduate level from institute Q?<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (a) 13:19\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 21:13\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 13:8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d)19:13<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0SOLUTION <\/strong><\/p>\n

                      1.(b):Students of institute M at graduate level = 17% of 27300 = 4641.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Students of institute S at graduate level = 14% of 27300 = 3822<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\Total number students at graduate level in institutes M and S = 4641+3822=8463\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                      2.(c):Required number = (15% of 24700) + (12% of 24700) = 3705 + 2964 = 6669.<\/p>\n

                      3.(d):Required number = (18% of 27300) + (14% of 24700) = 4914 + 3458 = 8372.<\/p>\n

                      4.(d):Required ratio =\u00a0 (21% of 24700) = 21 * 24700 = 19<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (14% of 27300)\u00a0\u00a0\u00a0 14 * 27300\u00a0\u00a0\u00a0\u00a0 14<\/p>\n

                      5.(d):Required ratio = (21% of 24700) = 21 * 24700 = 19<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ( 13% of 27300)\u00a0\u00a0\u00a0 13 * 27300\u00a0\u00a0\u00a0 13<\/p>\n

                      Example 4.Study the following pie-chart and the table and the answer the questions based on them<\/em><\/strong>.<\/p>\n

                      PROPORTION OF POPULATION OF SEVEN VILLAGES IN 1997<\/strong><\/p>\n

                       <\/p>\n\n\n\n\n\n\n\n\n\n\n
                      \n

                      village<\/p>\n<\/td>\n

                      		\n

                      % population below\u00a0\u00a0 poverty<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      X<\/p>\n<\/td>\n

                      		\n

                      38<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      Y<\/p>\n<\/td>\n

                      		\n

                      52<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      Z<\/p>\n<\/td>\n

                      		\n

                      42<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      R<\/p>\n<\/td>\n

                      		\n

                      51<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      S<\/p>\n<\/td>\n

                      		\n

                      49<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      T<\/p>\n<\/td>\n

                      		\n

                      46<\/p>\n<\/td>\n<\/tr>\n

                      \n

                      V<\/p>\n<\/td>\n

                      		\n

                      58<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                      1.Find the population of villages S if the population of village X below poverty line in 1997 is 12160.<\/p>\n

                      \u00a0\u00a0\u00a0 (a). 18500\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0(b) 20500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 22000\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 26000<\/p>\n

                      2.The ratio of the population of the village T below poverty line to that of village Z below poverty line in 1997 is:<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0 (a) 11:23\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 13:11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 23:11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 11:13<\/p>\n

                      3.If the population of village R in 1997 is 32000,then what will be the population of village Y below poverty line in that year?<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0 (a) 14100\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b)15600\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 16500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 17000<\/p>\n

                      4.If in 1998, the population of villages Y and V increases by 10% each and the percentage of population below poverty line remains unchanged for all the villages, then find the population of village V below poverty line in 1998,given that the population of village Y in 1997 was 30000.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (a) 11250\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b) 12760\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 13140\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 13780<\/p>\n

                      5.If in 1998,the population of village R increases by 10% while that of village Z reduces by 5% compared that in 1997 and the percentage of population below poverty line remains unchanged for all the village,then find the approximate ratio of population of village R below poverty line for the year 1999.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (a) 2:1\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (b)\u00a0 3:2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (c) 4:3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (d) 5:4<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 SOLUTION<\/strong><\/p>\n

                      1.(c):Let the population of village X be x<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Then,38% of x=12160\u00a0 \u00de\u00a0 x = 12160 * 100\u00a0\u00a0\u00a0\u00a0\u00a0 =3200<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 38<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Now ,if s be the population village S,then<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a011 * 32000<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16:11 = 32000 : s\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00de\u00a0 s=\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 22000.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 16<\/p>\n

                      2.(c): Let N be the total population of all the seven villages.<\/p>\n

                      Then ,population of village T below poverty line = 46% of (21% of N) and population of\u00a0\u00a0 village Z below poverty line = 42% of (11% of N)<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\Required ratio\u00a0\u00a0 =\u00a0\u00a0 46% of (21% of N)\u00a0\u00a0 =\u00a0\u00a0\u00a0\u00a0\u00a0 46 * 21\u00a0\u00a0 =\u00a0\u00a0\u00a0 23<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a042% of (11% of N)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 42 * 11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 11\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                      3.(b): Population of village R = 32000(given)<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Let the population of village Y be y.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Then, 16:15\u00a0 =\u00a0 32000 : y\u00a0\u00a0\u00a0\u00a0 \u00de\u00a0\u00a0\u00a0 y\u00a0 = 15 * 32000\u00a0\u00a0 =30000<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a016<\/p>\n

                      4.(b): Population of village Y in 1997\u00a0 =\u00a0 30000(given) .<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Let the population village V in 1997 be v.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Then, 15:10 = 30000:v\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00de\u00a0 v\u00a0 = 30000 * 10\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 20000.<\/p>\n

                      \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a015\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Now population of village V in 1998 = 20000 + (10% 0f 20000) = 20000.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\Population of village V below poverty line in 1998\u00a0 =\u00a0 58% of 22000 = 12760.<\/p>\n

                      5.(a) : Let the total population of all the seven villages in 1997 be N.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Then,population of village R in 1997 = 16% of N =\u00a0 16\/ 100 N<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 And population of village Z in 1997 = 11% of N =11\/100 N<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\Population of village R in 1999 = {16\/100N+(10% of 16\/100 N)}=1760\/10000 N<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 and population of village Z in 1999 = {11\/100 N-(5% of 11\/100 N)} = 1045\/10000 N.<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Now,population of village R below poverty line for 1999 = 51% of(1760\/10000 N)<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 And population of village Z below poverty line 1999 = 42% of (1045\/10000 n)<\/p>\n

                      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 51% of (1760\/10000 N)\u00a0\u00a0\u00a0\u00a0\u00a0 51 * 1760\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2<\/p>\n

                      Required ratio =\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ————————– =\u00a0 ————-\u00a0\u00a0 =\u00a0 ——\u00a0\u00a0\u00a0\u00a0<\/p>\n

                      \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a042% of (1045\/10000 N)\u00a0\u00a0\u00a0 42 * 1045\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n

                      “Quantitative Aptitude for Competitive Examinations” by R.S. Aggarwal is a comprehensive resource widely used by aspirants preparing for various competitive exams. The book includes a dedicated section on Pie Charts, offering detailed explanations and practice questions to enhance data interpretation skills.<\/p>\n

                      Accessing the Pie Charts Section:<\/strong><\/p>\n

                      While the complete book is available for purchase through authorized retailers, specific sections, such as the one on Pie Charts, can be accessed through the following resource:<\/p>\n

                        \n
                      • \n

                        UPSC Fever<\/strong>: This platform provides practice questions from R.S. Aggarwal’s Quantitative Aptitude, including those on Pie Charts. You can explore these questions here:<\/p>\n<\/li>\n<\/ul>\n

                        Important Consideration:<\/strong><\/p>\n

                        Accessing or downloading copyrighted material without proper authorization may infringe upon intellectual property rights. It’s always best to obtain study materials through legitimate channels to ensure compliance with legal and ethical standards.<\/p>\n

                        If you have specific questions or need further assistance with topics related to Pie Charts or other areas in quantitative aptitude, feel free to ask!<\/p>\n

                        RS Aggarwal Quantitative Aptitude PDF Free Download: PIE-CHARTS<\/h3>\n","protected":false},"excerpt":{"rendered":"

                        PIE-CHARTS IMPORTANT FACTS AND FORMULAE The pie-chart or a pie-graph is a method of representing a given numerical data in the form of sectors of a circle. The sectors of the circle are constructed in such a way that the area of each sector is proportional to the corresponding value of the component of the […]<\/p>\n","protected":false},"author":41,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[126,127],"tags":[],"class_list":["post-6049","post","type-post","status-publish","format-standard","hentry","category-rs-aggarwal-quantitative-aptitude","category-rs-aggarwal-quantitative-aptitude-pdf"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6049","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/users\/41"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/comments?post=6049"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6049\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/media?parent=6049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/categories?post=6049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/tags?post=6049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}