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# True Discount Questions

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Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

ARs. 7.19

BRs. 10.40

CRs. 12.07

DRs. 16

Explanation:

S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D. on Rs. 260 = Rs. $$\frac{10}{250} * 260$$ = Rs. 10.40

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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 ins Rs.40.what is the amount of the bill,if he money be worth 12$$\frac{1}{2}$$%?

A1200

B3000

C3600

D1300

Explanation:

Let the sum be Rs. x. Then,
$$\left[\frac{x}{2} + \frac{ \frac{x}{2} * 100}{100 + \left( \frac{25}{2} * 2\right)} \right] - \frac{x * 100}{100 + \left(\frac{25}{2} * 1 \right)}$$ = 40
or, $$\frac{x}{2} + \frac{2x}{5} - \frac{8x}{9}$$ = 40
or, x = Rs. 3600.
Therefore, amount of the bill = Rs. 3600.

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A has to pay Rs. 220 to B after 1 year. B asks A to pay Rs. 110 in cash and defer the payment of Rs. 110 for 2 years. A agrees to it. If the rate of interest be 10% per annum, in this mode of payment :

AThere is no gain or loss to any one

BA gains Rs. 7.34

CA loses Rs. 7.34

DA gains Rs. 11

Explanation:

Amount of money that A has to pay = P.W of Rs. 220 due 1 year hence

= Rs. $$\frac{220 * 100}{\left[ 100 + \left(10 * 1 \right)\right]}$$

= Rs. 200

Amount of money A actually pays = Rs. 110 + P.W of Rs. 110 due 2 years hence

= $$\frac{110 + \left( 110 * 100 \right)}{100 + \left(10 * 2\right)}$$

= Rs. 192.66

Therefore, A gains = Rs. ( 200 - 192.66 )

= Rs. 7.34

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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.

A1500

B1600

C6200

D6000

Explanation:

Let the amount of the bill be Rs. a

Then,

$$\left[\frac{a * r * t}{ 100 + ( r * t )}\right]$$ = T.D

or, $$\left[\frac{a * 12 * \frac{3}{4} } {100 + ( 12 * \frac{3}{4})}\right]$$ = 540

or, a = 540*$$\frac{109}{9}$$

or, a = Rs. 6540

Therefore, Amount = Rs. 6540

Hence, Present worth, P.W = Rs. ( 6540 - 540 )

= Rs. 6000

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The true discount on a certain sum of money due 3 year hence is Rs.100 and the S.I. on the same sum for the same time and at the same rate is Rs.120. Find the sum and the rate percent.

A(6 + $$\frac{2}{3}$$)%

B(5+ $$\frac{2}{3}$$)%

C(2+ $$\frac{2}{3}$$)%

D(4+ $$\frac{2}{3}$$)%

Explanation:

Sum can be calculated as,

S = $$\frac{S.I * T.D }{S.I - T.D}$$

= Rs. $$\left[\frac{120 * 100}{120 - 100}\right]$$

= Rs. 600

And, Rate = $$\left[\frac{100 * 120 }{ 600 x 3}\right]$$

= 6.667%

= (6 + $$\frac{2}{3}$$) %

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