True Discount Formula for Competitive Exams

Some of the students are ignored the true discount questions while preparing for competitive exams. But these questions are important for competitive exams. So, here I am sharing true discount formula for your better preparation.

True Discount Formula Questions

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 :

Sum due = Rs. 156 due 4 years hence;

Present Worth (P.W) = Rs. 100;

True Discount (T.D) = Rs. (156 – 100) = Rs. 56 = (Sum due) – (P.W)

We define : T.D = Interest on P.W

Amount = (P.W) + (T.D).

Interest is reckoned on P.W. and true discount is reckoned on the amount

Let rate = R% per annum and Time = T years. Then,

$$1. \ P.W. = {100×Amount\over100+(R+T)}= {100×T.D\over R×T} $$

  $$2. \ T.D = {(P.W)×R×T\over100}= {Amount×R×T\over100+(R+T)} $$

  $$3. \ Sum= {(S.I)×(T.D)\over(S.I)-(T.D)} $$

  $$4.\ (S.I)-(T.D)= S.I on T.D $$

  $$ When \ the \ sum \ is \ put \ at \ compound \ interest, \ then \ P.W = {Amount\over \left(1+{R\over100}\right)^T}$$

Q.1. Find the present worth of Rs. 930 due 3 years hence at 8% per annum. Also find the discount.

$$Solution$$

$$ \ P.W. = {100×Amount\over100+(R+T)}=Rs. {100×930\over 100×(8×3)}=Rs. {100×930\over 124}=Rs.750 $$

$$ T.D = (Amount)- (P.W)= Rs. (930-750)=Rs.180 $$

Q.2. The true discount on a certain sum of money due 3 years hence is Rs. 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.

$$Solution$$

$$\ T.D = Rs. 250 \ and \ S.I = Rs. 375.$$

$$∴ \ Sum \ due\ = {(S.I)×(T.D)\over(S.I)-(T.D)}={375×250\over375-250}= Rs. 750 $$

$$ Rate = \left({100×375\over750×3}\right)\% = 16{2\over3}\% $$

Q.3. The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:

$$Solution$$

$$ P.W = RS. (2562 - 122) = Rs. 2440$$

$$∴ S.I. on \ Rs. 2440 \ for \ months \ is \ Rs. 122$$

$$∴  Rate = \left({100×122\over{2440×{1\over3}}}\right)\% = 15\% $$

Q.4. The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is :

$$P.W. = Rs. (1760-160)= Rs. 1600 $$

   $$ ∴ S.I. on \ Rs. 1600 \ 12\% \ is \ Rs. \ 1600$$

   $$∴ Time = \left({100×160\over 1600×12 }\right)= {5\over6} \ years = \left({5\over6}×12\right) \ month = 10 \ months. $$

Q.5. The true discount on a bill due 9 month hence at 16% per annum is Rs. 189. The amount of the bill is :

$$ Let \ P.W \ be \ Rs.\ x. \ Then, S.I \ on \ Rs.x \ at \ 16\% \ for\ 9 \ months = Rs.189 $$

 $$∴ x× 16×  {9\over12}× {1\over100}=189 \ or \ x =1575.  $$

   $$∴ \ Sum\ due \ = P.W +T.D = Rs. (1575+189)= Rs. 1764. $$

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