{"id":5978,"date":"2025-06-09T09:39:10","date_gmt":"2025-06-09T09:39:10","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=5978"},"modified":"2025-06-09T09:39:10","modified_gmt":"2025-06-09T09:39:10","slug":"rs-aggarwal-quantitative-aptitude-pdf-partnership-download","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/rs-aggarwal-quantitative-aptitude-pdf-partnership-download\/","title":{"rendered":"RS Aggarwal Quantitative Aptitude PDF Free Download: PARTNERSHIP"},"content":{"rendered":"

PARTNERSHIP<\/strong><\/h1>\n

!IMPORTANT FACTS AND FORMULAE <\/u><\/strong>I<\/u><\/strong><\/h2>\n
    \n
  1. Partnership:<\/strong> When two or more than two persons run a business jointly, they are<\/li>\n<\/ol>\n

    \u00a0\u00a0\u00a0 called partners and the deal is known as partnership.<\/em><\/p>\n

    \u00a0<\/em>Ratio of Division of Gains:<\/strong><\/p>\n

      \n
    1. i) When investments of all the partners are for the same time, <\/em>the gain or loss is distributed a\u00a0 among the partners in the ratio of their investments.<\/li>\n<\/ol>\n

      Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:<\/p>\n

      (A\u2019s share of profit) : (B’s share of profit) = x : y.<\/p>\n

        \n
      1. ii) When investments are for different time periods, <\/em><\/strong>then equivalent capitals are calculated for a unit of time by taking (capital x number of units of time). Now, gain or loss is divided in the ratio of\u00a0 these capitals.<\/li>\n<\/ol>\n

        Suppose A invests Rs. x for p months and B invests Rs. y for q months, then<\/p>\n

        \u00a0(A\u2019s share of profit) : (B’s share of profit) = xp : yq.<\/em><\/p>\n

        \u00a0<\/strong>Working and Sleeping Partners:<\/strong> A partner who manages the business is known . as a working partner <\/em>and the one who simply invests the money is a sleeping <\/em>partner.<\/em><\/p>\n

        \u00a0<\/em>\u00a0SOLVED EXAMPLES <\/u><\/strong><\/p>\n

        Ex. 1. A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 <\/strong>and ,Rs.1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700. <\/strong><\/p>\n

        Sol.<\/strong> Ratio of shares of A, Band C = Ratio of their investments<\/p>\n

        = 120000 : 135000 : 150000 = 8 : 9 : 10.<\/p>\n

        A\u2019s share = Rs. (56700 x (8\/27))<\/u>= Rs. 16800.<\/p>\n

        B’s share = Rs. ( 56700 x (9\/27)) = Rs. 18900.<\/p>\n

        C’s share = Rs. ( 56700 x (10\/27))=<\/u>Rs. 21000.<\/p>\n

        \u00a0<\/strong>Ex. 2. Alfred started a business investing <\/strong>Rs. 45,000. After 3 months, Peter joined hi<\/strong>m with <\/strong>a capital of Rs. 60,000. After another 6 months, Ronald joined them with <\/strong>a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire <\/strong>of each.<\/strong><\/p>\n

        \u00a0<\/strong>\u00a0Sol.<\/strong> Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 for 3 months.<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)<\/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 = 540000 : 540000 : 270000 = 2 : 2 : 1.<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Alfred’s share = Rs. (16500 x (2\/5)) = Rs. 6600<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Peter’s share = Rs. (16500 x (2\/5)) = Rs. 6600<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Ronald’s share = Rs. (16500 x (1\/5)) <\/em>= Rs. 3300.<\/p>\n

        Ex. 3. A, <\/strong>Band C start a business each investing Rs. 20,000. <\/strong>After 5 months A\u00a0 withdrew Rs.6000\u00a0 B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.<\/strong><\/p>\n

        Sol.<\/strong> Ratio of the capitals of A, Band C<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= 205000:212000 : 282000 = 205 : 212 : 282.<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A\u2019s <\/em>share = Rs. 69900 x (205\/699) = Rs. 20500\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 I<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 B’s share = Rs. 69900 x (212\/699) = Rs. 21200;<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 C’s share = Rs. 69900 x (282\/699) = Rs. 28200.<\/p>\n

        Ex. 4. A, Band C enter into partnership. A invests 3 times as much as B<\/strong><\/p>\n

        and B invests two-third of what C invests. At the end of the year, the <\/strong>profit earned is Rs. 6600. What is the share of B ?<\/strong><\/p>\n

        Sol.<\/strong> Let C’s capital = Rs. x. Then, B’s capital = Rs. (2\/3)x<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A\u2019s <\/em>capital = Rs. (3 x (2\/3).x) <\/em>= Rs. 2x.<\/em><\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0 Ratio of their capitals = 2x <\/em>: (2\/3)x \ud83d\ude21 = 6 : 2 : 3.<\/p>\n

        \u00a0\u00a0\u00a0\u00a0 Hence, B’s share = Rs. ( 6600 x (2\/11))= Rs. 1200.<\/p>\n

        Ex. 5. Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for\u00a0 5 months; C 35 cows for 4 months and D 21 cows for 3 months. <\/strong>If A’s share of rent is Rs. 720, find the total rent of the field.<\/strong><\/p>\n

        \u00a0<\/strong>Sol.<\/strong> Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) \u00a0 = 72 : 50 : 140 : 63.<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Let total rent be Rs. x. Then, A\u2019s <\/em>share = Rs. (72x)\/325<\/p>\n

        \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(72x)\/325=720 \u00f3 x=(720 x 325)\/72 = 3250\u00a0\u00a0\u00a0<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Hence, total rent of the field is Rs. 3250.<\/p>\n

        Ex.6. A invested Rs. 76,000 in a business. After few months, B joined <\/strong>him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio\u00a0 2 : 1. After bow many months did B join?<\/strong><\/p>\n

        Sol. Suppose B joined after x months. Then, B’s money was invested for (12 – x)<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (76000 x 12)\/(57000 x (12-x) =2\/1 \u00f3 912000=114000(12-x)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/em><\/p>\n

        \u00a0114 (12 – x) = 912\u00f312-x=8\u00f3x=4<\/p>\n

        \u00a0Hence, B joined after 4 months.<\/p>\n

        Ex.7. A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.<\/strong><\/p>\n

        \u00a0<\/strong>Sol. Let the initial investments of A, Band C be Rs. 3x, <\/em>Rs. 2x and Rs. 4x respectively. Then,<\/p>\n

        (3x <\/em>x 36) : [(2x <\/em>x 12) + (2x <\/em>+ 270000) x 24] : [(4x <\/em>x 24) + (4x <\/em>+270000) x 12]=3:4:5<\/p>\n

        1O8x<\/em> : (72x <\/em>+ 6480000) : (144x <\/em>+ 3240000) = 3 : 4 : 5<\/p>\n

        \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 108x \/(72x+6480000)=3\/4\u00a0 \u00f3 432x <\/em>= 216x <\/em>+ 19440000<\/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 <\/em>\u00f3216x <\/em>= 19440000\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 x=90000<\/p>\n

        Hence, A\u2019s initial investment = 3x = Rs. 2,70,000;<\/p>\n

        \u00a0\u00a0 B’s initial investment = 2x = Rs. 1,80,000;<\/p>\n

        \u00a0\u00a0 C’s initial investment = 4x = Rs. 3,60,000.<\/p>\n

        I understand you’re seeking the “Partnership” chapter from R.S. Aggarwal’s Quantitative Aptitude<\/em> book. This book is widely used for competitive exam preparation and is available for purchase through various retailers.<\/p>\n

        Where to Purchase:<\/strong><\/p>\n