True Discount
 If the interest on Rs. 50 at 4^{1}/_{2} be equal to the discount on Rs. 59 for the same time and at the same rate when is the latter sum due ?

 2 years
 4 years
 6 years
 3 years

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∵ 9 / 2 = 59  50 / 50 x T x 100
∴ T = 4 yearsCorrect Option: B
∵ 9/2 = [(59  50) x 100] / 50 x T
∴ T = 4 years
 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 ?

 Rs. 500
 Rs. 200
 Rs. 250
 Rs. 100

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Sum = [(S.I.) x (T.D.)] / [(S.I.)  (T.D.)] = Rs. (25 x 20) / (25  20)
= Rs. 100Correct Option: D
Sum = [(S.I.) x (T.D.)] / [(S.I.)  (T.D.)] = Rs. (25 x 20) / (25  20)
= Rs. 100
 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?

 Rs. 30900
 Rs. 39000
 Rs. 20900
 Rs. 30600

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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
 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 ?

 Gains Rs. 15
 Gains Rs. 3
 Gains Rs. 5
 Loses Rs. 5

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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
 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?

 ₹ 100
 ₹ 32
 ₹ 86
 ₹ 96
 None of the above

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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