## True Discount

#### True Discount

1. If the interest on Rs. 50 at 41/2 be equal to the discount on Rs. 59 for the same time and at the same rate when is the latter sum due ?
1. 2 years
2. 4 years
3. 6 years
4. 3 years

1. ∵ 9 / 2 = 59 - 50 / 50 x T x 100
∴ T = 4 years

##### Correct Option: B

∵ 9/2 = [(59 - 50) x 100] / 50 x T
∴ T = 4 years

1. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 25 and Rs. 20 respectively. The sum is ?
1. Rs. 500
2. Rs. 200
3. Rs. 250
4. Rs. 100

1. Sum = [(S.I.) x (T.D.)] / [(S.I.) - (T.D.)] = Rs. (25 x 20) / (25 - 20)
= Rs. 100

##### Correct Option: D

Sum = [(S.I.) x (T.D.)] / [(S.I.) - (T.D.)] = Rs. (25 x 20) / (25 - 20)
= Rs. 100

1. The difference between the simple interest and the true discount on a certain sum of money for 6 months at 6% is Rs. 27. Find the sum?
1. Rs. 30900
2. Rs. 39000
3. Rs. 20900
4. Rs. 30600

1. Req. amount = [27 x (100 + 6 x 1/2) x 100] / [(6 x 1/2)2]

##### Correct Option: A

Req. amount = [27 x (100 + 6 x 1/2) x 100] / [(6 x 1/2)2]
= (2700 x 103) / 9 = Rs. 30900

1. A man buys a watch for Rs. 195 in cash and sells it for Rs. 220 at a credit of 1 year. If the rate of interest is 10%, the man ?
1. Gains Rs. 15
2. Gains Rs. 3
3. Gains Rs. 5
4. Loses Rs. 5

1. P.W. of Rs. 220 due 1 year hence = Rs. (100 x 220) / (100 + 10)

##### Correct Option: C

P.W. of Rs. 220 due 1 year hence = Rs. (100 x 220) / (100 + 10)
= Rs. 200
hence, the man gains Rs. 5

1. What will be the true discount for the present worth of ₹ 600 for a period of 4 yr at 4% per annum rate of interest?
1. ₹ 100
2. ₹ 32
3. ₹ 86
4. ₹ 96
5. None of the above

1. TD = (PW x R x T)/100

##### Correct Option: D

Given that, T = 4 yr, R = 4%
PW = ₹ 600 and TD = ?
According to the formula, (1)
TD = (PW x R x T)/100
TD = (600 x 4 x 4)/100 = 6 x 4 x 4 = ₹ 96