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
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    ∵ 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

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  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
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    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

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

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  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
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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

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  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
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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

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