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Aptitude::True Discount

Home > Quantitative Aptitude > True Discount > Subjective Solved Examples

Example 1 / 8

Find the present worth of Rs. 930 due 3 years hence at 8% per annum. Also, find the discount.
P.W. = \(\frac{100 \times Amount}{100 + (R \times T)}\) = Rs\([\frac{100 \times 930}{100 + (8 \times 3)}]\) = Rs. \(\frac{100 \times 930}{124}\) = Rs. 750.
T.D. = (Amount) – (P.W.) = Rs. (930 -750) = Rs. 180.Ans.
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Example 2 / 8

If the true discount on a sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:
P.W. = \(\frac{100 \times T.D.}{R \times T}\) = \(\frac{100 \times 168}{14 \times 2}\) = 600
Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs.768 Ans.
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Example 3 / 8

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. Find the amount of the bill and its present worth:
Let amount be Rs. x.

Then, interest on (P.W) Rs. x at 16% for 9 months = Rs. 189.

=> \(\frac{x \times 16 \times \frac{9}{12}}{100 + \left(16 \times \frac{9}{12}\right)}\) = 189

=> \(\frac{x \times 16 \times \frac{3}{4}}{100 + \left(16 \times \frac{3}{4}\right)}\) = 189

=> \(\frac{x \times 12}{100 + 12}\) = 189

=> x = \(\frac{189 \times 112}{12}\)
=> x (Amount) = Rs. 1764.

=> P.W. = Rs. \(\left(1764 - 189\right)\) = Rs. 1575.Ans.
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Example 4 / 8

If the true discount on a sum due 2 years hence at 14% per annuum be Rs. 168, the sum due is:
P.W. = \(\frac{100 \times T.D.}{R \times T}\) = \(\frac{100 \times 168}{14 \times 2}\) = 600.

Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs. 768.
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Example 5 / 8

If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

S.I on Rs. (110 -10) for a certain time = Rs. 10.

S.I. on Rs. 100 for double the time = Rs. 20.

T.D. on Rs. 120 = Rs. (120 -100) = Rs. 20.

T.D. on Rs. 110 = Rs. (\(\frac{20}{120}\) x 110) = Rs. 18.33.Ans.
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Example 6 / 8

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
Given, T.D.(True Discount) = Rs. 250 and S.I.(Simple Interest) = Rs. 375.

Sum due = \(\frac{S.I. \times T.D}{(S.I.) – (T.D.)}\)

= Rs. \(\left(\frac{375 \times 250}{375 – 250}\right)\) = Rs. 750.

Rate = \(\left(\frac{100 \times 375}{750 \times 3}\right)\)% = 16\(\frac{2}{3}\)%
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Example 7 / 8

The difference between the simple interest and true discount on a certain sum of money for 6 months at 12\(\frac{1}{2}\)% per annum is Rs. 30. Find the sum?
Given,
Time = 6 months =\(\frac{1}{2}\) of year.
Rate = 12\(\frac{1}{2}\)% = \(\frac{25}{2}\)%
Consider,
True discount = \(\frac{A * R * T}{100 + (R * T)}\)
⇒ True discount = \(\frac{x * \frac{25}{2} * \frac{1}{2}}{100 + (\frac{25}{2} * \frac{1}{2})}\)
⇒ True discount = \(x * \frac{25}{4} * \frac{4}{425}\)
⇒ True discount = \(\frac{25x}{425}\)
⇒ True discount = \(\frac{x}{17}\)
Now,
Simple interest = (\(x * \frac{25}{2} * \frac{1}{2} * \frac{1}{100})\)
⇒ Simple interest = \(\frac{x}{16}\)
Therefore,
\(\frac{x}{16}\) – \(\frac{x}{17}\) = 30.
⇒ 17\(x\) – 16\(x\) = 30 * 16 * 17
⇒ \(x\) = 8160
Therefore, sum due = Rs. 8160.Ans.
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Example 8 / 8

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 gains Rs. 50. What is the amount of the bill, if the money be worth 12\(\frac{1}{2}\)%?
Let the sum be \(x\). Then,
⇒ \(\left[ \frac{x}{2} + \frac {\frac{x}{2} * 100} {100 + (\frac{25}{2} * 2)} \right] \)– \(\frac{x * 100}{100 + (\frac{25}{2} * 1)}\) = 50.
⇒ \(\frac{x}{2} + \frac{2x}{5} – \frac{8x}{9}\) = 50.
⇒ \(\frac{45x + 36x – 80x}{90}\) = 50
⇒ \(\frac{x}{90}\) = 50
⇒ \(x\) = 4500.
Therefore, amount of the bill = Rs. 4500.Ans.
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