True Discount
- The true discount on Rs. 1860 due 3 years hence is Rs. 40. Find the rate per cent ?
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R = (100 x T.D.) / (P.W. x T) = (100 x T.D.) / [(A - T.D.) x T]
= (100 x 60) / (1800 x 3) [ since P.W. = A - T.D.]Correct Option: A
R = (100 x T.D.) / (P.W. x T) = (100 x T.D.) / [(A - T.D.) x T]
= (100 x 60) / (1800 x 3) [ since P.W. = A - T.D.]
= 10%
∴ The rate per cent is 10% per annum
- Goods were bought for Rs. 600 and sold the same day for Rs. 650.25 at a credit of 9 month and still there was a gain of 2%. The rate percent is ?
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S.P. = (102% of Rs. 600) = Rs. (102/100) x 600 = Rs. 612
∴ P.W. of Rs. 650.25 due 9 months later is Rs. 612.
⇒ Rs. 38.25 is S.I. on Rs. 612 for 9 months
∴ Rate = (100 x 38.25) / (612 x 3/4)%Correct Option: B
S.P. = (102% of Rs. 600) = Rs. (102/100) x 600 = Rs. 612
∴ P.W. of Rs. 650.25 due 9 months later is Rs. 612.
⇒ Rs. 38.25 is S.I. on Rs. 612 for 9 months
∴ Rate = (100 x 38.25) / (612 x 3/4)% = 81/3%
- If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time. Then the discount allowed on the same sum due at the end of double the time is ?
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S.I. on Rs. (110 - 10) for a given time = Rs. 10
S.I. on Rs. 100 for double the time = 20
Sum = Rs. (100 + 20) = Rs. 120
T.D. on Rs. 110 = Rs. (20 /120) x 110Correct Option: D
S.I. on Rs. (110 - 10) for a given time = Rs. 10
S.I. on Rs. 100 for double the time = 20
Sum = Rs. (100 + 20) = Rs. 120
T.D. on Rs. 110 = Rs. (20 /120) x 110 = Rs. 18.33
- If the true discount on Rs. 161 due 21/ years hence be Rs. 21. At what rate per cent is the interest calculated ?
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Required rate percent = (100 x 21) / {(161 - 21) x 21/2}
Correct Option: A
Required rate percent = (100 x 21) / {(161 - 21) x 21/2} = 6%
- The present worth of a bill due 7 months hence is Rs. 1200 and if the bill were due at the end of 21/2 years, its present worth would be Rs. 1016. Find the rate percent and the sum of the bill ?
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∵ 1200/1016 = (100 + R x 5/2) / (100 + R x 7/12)
⇒ 1200 x (100 + R x 7/12) = 1016 x (100 + R x 5/2)
⇒ 3680 x R = 36800
∴ R = 10%Correct Option: A
∵ 1200/1016 = (100 + R x 5/2) / (100 + R x 7/12)
⇒ 1200 x (100 + R x 7/12) = 1016 x (100 + R x 5/2)
⇒ 3680 x R = 36800
∴ R = 10%
∴ Sum due = 1200 + S.I. on Rs. 1200 for 7 months at 10%. = Rs. 1270
