Problem solving tricks on sales and discount

IMPORTANT CONCEPTS

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that:

Sum due = Rs. 156 due 4 years hence;

Present Worth (P.W.) = Rs. 100;

True Discount (T.D.) = Rs. (156 – 100) = Rs. 56 = (Sum due) – (P.W.)

We define: T.D. = Interest on P.W.;     Amount = (P.W.) + (T.D.)

Interest is reckoned on P.W. and true discount is reckoned on the amount.

IMPORTANT FORMULAE

Let rate = R% per annum and Time = T years. Then,

1.   P.W. = 100 x Amount = 100 x T.D.
100 + (R x T) R x T
2.   T.D. = (P.W.) x R x T = Amount x R x T
100 100 + (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 T
100
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%

Answer: Option A

Explanation:

C.P. = Rs. 3000.

S.P. = Rs. 3600 x 100 = Rs. 3000.
100 + (10 x 2)

Gain = 0%.

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. Rs. 9025.20
B. Rs. 9200
C. Rs. 9600
D. Rs. 9560

Answer: Option B

Explanation:

Required money = P.W. of Rs. 10028 due 9 months hence
= Rs. 10028 x 100
100 + 12 x 9
12
= Rs. 9200.

The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:

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

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?

The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:

The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:

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