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Important Formulae

Let rate = R% per annum and Time = T years, T. D. = True Discount, P. W. = Present Worth Then,
1. P.W. = 100 x Amount/100 + (R x T) = 1100 x T.D./(R x T)
2. T.D. = (P.W.) x R x T./100 = Amount x R x T/100 + (R x T)
3. Sum = (S.I.) x (T.D.)/(S.I.) - (T.D.)
4. (S.I.) - (T.D.) = S.I. on T.D.
5. When the sum is put at compound interest, then P.W. = Amount/(1 + R/100)T

Practice Questions

1.

 A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of: A.0% B.5% C.7.5% D.10%

C.P. = Rs. 3000
S.P. = Rs.[(3600 x 100)/(100) + (10 x 2)] = Rs. 3000.
Gain = 0%.

2.

 The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is: A.12% B.13% C.15% D.14%

P.W. = Rs. (2562 - 122) = Rs. 2440.
S.I. on Rs. 2440 for 4 months is Rs. 122.
Rate = [(100 x 122)/(2440 x 1/3)]% = 15%

3.

 A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay? A.9025.50 B.9200 C.9600 D.9560.20

Required money= P.W. of Rs. 10028 due 9 months hence =
Rs.[(10028 x 100)/(100 + 12 x (9/12)] = Rs. 9200.

4.

 A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer? A.12,000 in cash B.12,880 at credit C.Both are equally good D.Nil

P.W. of Rs. 12,880 due 8 months hence= Rs.[(12880 x 100)/(100 + 18 x (8/12)]
P.W. of Rs. 12,880 due 8 months hence = Rs. (12880 x 100)/112
P.W. of Rs. 12,880 due 8 months hence = Rs. 11500

5.

 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: A.20 B.21.80 C.22 D.18.33

S.I. on Rs. (110 - 10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20.
T.D. on Rs. 110 = Rs.(20/120) x 110 = Rs. 18.33

6.

 Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is: A.16(2/3)% B.14(1/2)% C.13(1/3)% D.15%

S.P. = 102% of Rs. 600 = [(102/100) x 600] = Rs. 612.
Now, P.W. = Rs. 612 and sum = Rs. 688.50.
T.D. = Rs. (688.50 - 612) = Rs. 76.50.
Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.
Rate = [(100 x 76.50)/(612 x 3/4)]% = 16(2/3)%

7.

 The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is: A.1386 B.1764 C.1575 D.2268

Let P.W. be Rs. X
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
X x 16 x (9/12) x (1/100) = 189 or X = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.

8.

 A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man: A.Gains Rs. 55 B.Gains Rs. 50 C.Gains Rs. 30 D.Loses Rs. 30

S.P.= P.W. of Rs. 2200 due 1 year hence = Rs. [(2200 x 100)/(100 + (10 x 1))]
S.P.= P.W. of Rs. 2200 due 1 year hence = Rs. 2000.
Gain = Rs. (2000 - 1950) = Rs. 50.