{"id":6031,"date":"2025-06-09T11:21:30","date_gmt":"2025-06-09T11:21:30","guid":{"rendered":"https:\/\/thecompanyboy.com\/?p=6031"},"modified":"2025-06-09T11:21:30","modified_gmt":"2025-06-09T11:21:30","slug":"rs-aggarwal-quantitative-aptitude-pdf-download-discount-true","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/drive\/rs-aggarwal-quantitative-aptitude-pdf-download-discount-true\/","title":{"rendered":"RS Aggarwal Quantitative Aptitude PDF Free Download: TRUE DISCOUNT"},"content":{"rendered":"

TRUE DISCOUNT<\/strong><\/h1>\n

IMPORTANT CONCEPTS<\/strong><\/h2>\n

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs. 156 due 4 years hence. We say that:<\/p>\n

Sum due = Rs. 156 due 4 years hence;<\/p>\n

Present Worth (P.W.) = Rs. 100;<\/p>\n

True Discount (T.D.) = Rs. (156 – 100) = Rs. 56<\/p>\n

\u00a0(Sum due) – (P.W.).<\/p>\n

We define :\u00a0 T.D. = Interest on P.W.<\/p>\n

Amount = (P.W.) + (T.D.).<\/p>\n

\u00a0Interest is reckoned on P.W. and true discount is reckoned on the amount.<\/p>\n

IMPORTANT FORMULAE<\/h2>\n

Let rate = R% per annum and Time = T years. Then,<\/p>\n

    \n
  1. W.=[100 x Amount \/100 + (R x T)<\/li>\n<\/ol>\n

    \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 =100 x T.D.\/ RxT<\/p>\n

      \n
    1. T.D.=[(P.W.) x R x T \/100]<\/li>\n<\/ol>\n

      \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = [ Amount x RxT\/100 + (R x T)]<\/p>\n

      3.(S.I.)*(T.D.) \/(S.I.)-(T.D.)<\/p>\n

        \n
      1. (S.I.) – (T.D.) – S.I. on T.D.<\/li>\n
      2. When the sum is put at compound interest, then<\/li>\n<\/ol>\n

        \u00a0P.W. = Amount\/[1 +R\/100]^T<\/p>\n

        SOLVED EXAMPLES<\/h2>\n

        Ex. 1. Find the present worth of Rs. 930 due 3 years hence at 8% per annum. Also find the discount.<\/p>\n

        Sol.<\/p>\n

        \u00a0P.W=100 x Amount \/[100 + (R x T)]<\/p>\n

        =Rs.100 x 930\/100+ (8×3)<\/p>\n

        = (100×930)\/124<\/p>\n

        \u00a0= Rs. 750,<\/p>\n

        T.D. = (Amount) – (P.W.) = Rs. (930 – 750) = Rs. 180.<\/p>\n

        Ex. 2. The true discount on a bill due 9 months hence at 12% per annum is Rs. Find the amount of the bill and its present worth.<\/p>\n

        Sol.<\/strong>\u00a0\u00a0\u00a0 Let amount be Rs. x. Then,<\/p>\n

        x*R*T\/100 + (R x T)<\/p>\n

        =T.D.<\/p>\n

        =>x * 12*3\/ 4\/[100+[12*3\/4]]<\/p>\n

        =540<\/p>\n

        x= 540×109\u00a0 = Rs.6540<\/p>\n

        Amount – Rs. 6540. P.W. = Rs. (6540 – 540) – Rs. 6000.<\/p>\n

        Ex. 3. The true discount on a certain sum of money due 3 years hence is Rb. 250 and the simple interest on the same sum for the same time and at the same rate is Rs. 375. Find the sum and the rate percent.<\/p>\n

        Sol.<\/strong>\u00a0\u00a0\u00a0 T.D. = Rs. 250 and S.I. = Rs. 375.<\/p>\n

        Sum due =S.I. xT.D.\/ S.I. -T.D.<\/p>\n

        =375×250\/375- 250\u00a0\u00a0<\/p>\n

        =Rs.750.<\/p>\n

        Rate=[100*375\/750*3]%=16 2\/3%<\/p>\n

        Ex. 4. The difference between the simple interest and true discount on a certain sum<\/strong><\/p>\n

        of money for 6 months at 12\u2014% per annum is Rs. 25. Find the sum.<\/strong><\/p>\n

        Sol.<\/strong>\u00a0\u00a0\u00a0 Let the sum be Rs. x. Then,<\/p>\n

        T.D. = (x*25\/2*1\/2)\/(100+(25\/2*1\/2))=x*25\/4*4\/425=x\/17<\/p>\n

        S.I=x*25\/2*1\/2*1\/100=x\/16<\/p>\n

        x\/16-x\/17=25<\/p>\n

        =>17x-16x=25*16*17<\/p>\n

        =>x=6800<\/p>\n

        Hence, sum due = Rs. 6800.<\/p>\n

        Ex. 5. A bill falls due in 1 year. The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years. By this arrangement<\/strong><\/p>\n

        ins Rb. 40. What is the amount of the bill, if the money be worth 12-z% ?<\/p>\n

        Sol.<\/strong>\u00a0\u00a0\u00a0 Let the sum be Rs. x. Then,<\/p>\n

        [x\/2+(x\/2*100)\/100+(25\/2*2)]-[(x*100)\/(100+25\/2*1]<\/p>\n

        =40<\/p>\n

        =>x\/2+2x\/5-8x\/9=40<\/p>\n

        =>x=3600<\/p>\n

        Amount of the bill – Rs. 3600.<\/p>\n

        I can’t provide a free PDF download of Quantitative Aptitude<\/em> by R.S. Aggarwal, as it is copyrighted material. However, here are some legal ways to access the True Discount<\/strong> chapter:<\/p>\n

        Legal Ways to Access the Book:<\/strong><\/h3>\n
          \n
        1. Official Publisher Website<\/strong> \u2013 Check S. Chand Publishing.<\/li>\n
        2. Google Books & Amazon Kindle<\/strong> \u2013 Some sections may be available for preview or purchase.<\/li>\n
        3. Library Services<\/strong> \u2013 Public or university libraries may have a digital or physical copy.<\/li>\n
        4. Educational Platforms<\/strong> \u2013 Websites like Unacademy, BYJU\u2019S, and Gradeup provide free explanations and practice problems.<\/li>\n<\/ol>\n

          Need Help with True Discount?<\/strong><\/h3>\n

          I can explain the concept, provide formulas, and give you practice problems with solutions. Let me know what you need!<\/p>\n

          RS Aggarwal Quantitative Aptitude PDF Free Download: TRUE DISCOUNT<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

          TRUE DISCOUNT IMPORTANT CONCEPTS Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs. 156 due 4 years […]<\/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-6031","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\/6031","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=6031"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/posts\/6031\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/media?parent=6031"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/categories?post=6031"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/drive\/wp-json\/wp\/v2\/tags?post=6031"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}