text: 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
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