True Discount
- Find the present worth (PW) and the true discount reckoning 6% per annum simple interest of Rs. 176 due in 20 months time ?
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P.W. = (100 x 176) / (100 + (6 x 20)/12) = Rs. 160
T.D. = Amount - present worthCorrect Option: A
P.W. = (100 x 176) / (100 + (6 x 20)/12) = Rs. 160
T.D. = Amount - present worth
= Rs. 176 - Rs. 160 = Rs. 16
- The true discount on Rs. 2575 due 4 months hence is Rs. 75. The rate percent is ?
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P.W. = Rs. (2575 - 75) = Rs. 2500
∴ Rate = (100 x 75 x 3) / (2500 x 1)%Correct Option: C
P.W. = Rs. (2575 - 75) = Rs. 2500
∴ Rate = (100 x 75 x 3) / (2500 x 1)% = 9%
- What sum will discharge a debt of Rs. 5300 due a year and a half hence at 4% per annum ?
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Required sum = (100 x 5300) / {(100 + (3/2) x 4)}
Correct Option: A
Required sum = (100 x 5300) / {(100 + (3/2) x 4)}
= (100 x 5300) / 106 = Rs. 5000
- A man purchased a cow for Rs. 300 and sold it the same day for Rs. 360, allowing the buyer at the credit of 2 years. If the rate of interest be 71/2% per annum, then the man has a gain of ?
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P.W. of Rs. 360 due 2 years hence at 71/7% per annum
= Rs. { {100 x 360} / {100 + (50/7 x 2)}}
= Rs. { (100 x 360 x 7) / 800} = Rs. 315
∴ S.P. = Rs. 315
Hence, gain % = (15 x 100) / 300Correct Option: D
P.W. of Rs. 360 due 2 years hence at 71/7% per annum
= Rs. { {100 x 360} / {100 + (50/7 x 2)}}
= Rs. { (100 x 360 x 7) / 800} = Rs. 315
∴ S.P. = Rs. 315
Hence, gain % = (15 x 100) / 300 = 5%
- A owes B, Rs. 1120 payable 2 years hence and B owes A, Rs. 1081.50 payable 6 months hence. If they decide to settle their accounts forthwith by payment of ready money and the rate of interest be 6% per annum, then who should pay and how much ?
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P.W. of Rs. 1120 due 2 years hence at 6%
= Rs. [{100 x 1120} / {100 + (6 x 2)}] = Rs. 1000
P.W. of Rs. 1081.50 due 6 months hence at 6%
= Rs. [ {100 x 1081.50} / {100 + (6 x 1/2)} ]
= Rs [ (100 x 1081.50) / 103 ] = Rs. 1050
So, A owes B, Rs. 1000 cash and B owes A Rs. 1050 cash.Correct Option: B
P.W. of Rs. 1120 due 2 years hence at 6%
= Rs. [{100 x 1120} / {100 + (6 x 2)}] = Rs. 1000
P.W. of Rs. 1081.50 due 6 months hence at 6%
= Rs. [ {100 x 1081.50} / {100 + (6 x 1/2)} ]
= Rs [ (100 x 1081.50) / 103 ] = Rs. 1050
So, A owes B, Rs. 1000 cash and B owes A Rs. 1050 cash.
∴ B must pay Rs. 50 to A.
