Question 1

The present worth of a bill due 7 months hence is Rs. 1200 and if the bill were due at the end of 2 1/ 2 years, its present worth would be Rs. 1016. Find the rate percent and the sum of the bill?

Accepted Answer

∵ 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

Question 2

If the true discount on Rs. 161 due 2 1/ years hence be Rs. 21. At what rate per cent is the interest calculated?

Accepted Answer

Required rate percent = (100 x 21) / {(161 - 21) x 21/2} = 6%

Question 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?

Accepted Answer

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

Question 4

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?

Accepted Answer

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%

Question 5

The true discount on Rs. 1860 due 3 years hence is Rs. 40. Find the rate per cent?

Accepted Answer

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

Question 6

The interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810 for the same time and at the same rate. The rate percent is?

Accepted Answer

Since T.D. is S.I. on Rs. P.W., we have Rs. (810 - 750) or Rs. 60 as S.I. on Rs. 750 for 2 years ∴ Rate = (100 x 60) / (750 x 2) = 4%

Question 7

A trader owes a merchant Rs. 901 due 1 year's hence. However, the trader wants to settle the account after 3 months. How much cash should he pay, If rate of interest is 8% per annum?

Accepted Answer

P.W. of Rs. 901 due 9 months hence at 8% = Rs { (100 x 901) / (100 + (8 x 3 / 4))} = Rs. (100 x 901) / 106 = Rs. 850

Question 8

I want to sell my scooter. There are two offers, One at cash payment of Rs. 8100 and another at a credit of Rs. 8250 to be paid after 6 months. If money being worth 6 1/ 4% per annum simple interest, which is the better offer?

Accepted Answer

P.W. of Rs. 8285 due 6 months hence = Rs. { (100 x 8250) / {100 + (25 / 4 x 1 / 2)} } = Rs. 8000 ∴ Rs. 8100 in cash is a better offer.

Question 9

A has to pay Rs. 220 to B after 1 year. B asks A to pay Rs. 110 in cash and defer the payment of Rs. 110 for 2 years. A agrees to it. Counting the rate of interest at 10% per annum in this new mode of payment?

Accepted Answer

A has to pay the P.W. of Rs. 220 due 1 year hence, which is = Rs. [ (100 x 220) / {100 + (10 x 1)} ] = Rs. 200 A, actually pays = Rs. [110 + P.W. of Rs. 110 due 2 years hence] = Rs. [ 110 + (100 x 110) / {100 + (10 x 2)} ] = Rs. [110 + 91.66] = Rs. [201.66] ∴ A loses = Rs. [200 - 201.66] = Rs. 1.66

Question 10

Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Accepted Answer

S.I. on Rs. 240 for a given time = Rs. 20 S.I. on Rs. 240 for half the time = Rs. 10 ∴ Rs. 10 is T.D. on Rs. 250 So, T.D. on Rs. 260 = Rs. (10 / 250) x 260 = Rs. 10.40

Question 11

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?

Accepted Answer

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.

Question 12

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 7 1/ 2% per annum, then the man has a gain of?

Accepted Answer

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%

Question 13

What sum will discharge a debt of Rs. 5300 due a year and a half hence at 4% per annum?

Accepted Answer

Required sum = (100 x 5300) / {(100 + (3/2) x 4)} = (100 x 5300) / 106 = Rs. 5000

Question 14

The true discount on Rs. 2575 due 4 months hence is Rs. 75. The rate percent is?

Accepted Answer

P.W. = Rs. (2575 - 75) = Rs. 2500 ∴ Rate = (100 x 75 x 3) / (2500 x 1)% = 9%

Question 15

Find the present worth (PW) and the true discount reckoning 6% per annum simple interest of Rs. 176 due in 20 months time?

Accepted Answer

P.W. = (100 x 176) / (100 + (6 x 20)/12) = Rs. 160 T.D. = Amount - present worth = Rs. 176 - Rs. 160 = Rs. 16

Question 16

The true discount on Rs. 1860 due after a certain time at 5% is Rs. 60. The time after which it is due is?

Accepted Answer

P.W. = (Sum due) - (T.D.) = Rs. (1860 - 60) = Rs. 1800 Thus, Rs. 60 is S.I. on Rs. 1800 at 5% per annum ∴ Time = (100 x 60) / (1800 x 5) years = 2 / 3 years = 8 months

Question 17

The true discount on a bill a due 8 months hence at 12% per annum is Rs. 240. Find the amount of the bill and its present worth?

Accepted Answer

P.W. = (100 x T.D.) / (R x T) = (100 x 240) / (12 x 8/12) = Rs. 3000 ∵ P.W. is Rs. 3000 ∴ A = Amount of bill = P.W. + T.D. = 3000 + 240 = 3240

Question 18

The difference between the simple interest and the true discount on a certain sum for 6 months at 4% is Rs. 15. Find the sum?

Accepted Answer

∵ 15 = [A x (4 x 1/2)2] / [100(100 + 4 x 1/2)] ⇒ 15 = (A x 4) / (100 x 102) ⇒ A = 15 x 25 x 102 ∴ A = Rs. 38, 250.

Question 19

Find the difference between simple interest and true discount on Rs. 960 due 4 year hence at 5% per annum simple interest?

Accepted Answer

S.I. - T.D. = [A x (R.T)2] / [100(100 + R.T.)] = [960 x (4 x 5)2] / [100 x (100 + 4 x 5)] = [(960 x 20 x 20) / (100 x 120)] = Rs. 32

Question 20

What will be the present worth of ₹ 3720 due 3 yr hence at 8% per annum? Also, find the true discount.

Accepted Answer

Let PW be N. ∴ 3720 - N = (N x 8 x 3) / 100 = 6N / 25 ⇒ 31N = 3720 x 25 ∴ N = (3720 x 25) / 31 = ₹ 3000 TD = Amount - PW = 3720 - 3000 = ₹ 720

True Discount Questions