# True Discount Questions

FACTS  AND  FORMULAE  FOR  TRUE  DISCOUNT  QUESTIONS

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 Rs. 156 in 4 years. So, the payment of Rs. 100 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) = (Sum due) - (P.W)=Rs. (156 - 100) = Rs. 56

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.$\inline P.W = \frac{100\times Amount}{100+(R\times T)}=\frac{100\times T.D}{R\times T}$

2. $\inline T.D = \frac{(P.W)\times R\times T}{100}=\frac{Amount\times R\times T}{100+(R\times T)}$

3.  $\inline Sum = \frac{(S.I)\times (T.D)}{(S.I)-(T.D)}$

4. (S.I) - (T.D )= S.I on T.D

5. When the sum is put at compound interest, then

$\inline P.W=\frac{Amount}{(1+\frac{R}{100})^T}$

Q:

The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?

 A) 715 B) 469 C) 400 D) 750

Explanation:

Let C.P be Rs. x

900 - x = 2(x - 450)

=> x = Rs.600

C.P = 600 gain required is 25%

S.P = [(100+25)*600]/100

= Rs.750

18 12034
Q:

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) loses Rs. 30 D) gains Rs. 30

Explanation:

12 10380
Q:

The difference between Simple Interest and True Discount on a certain sum of money for 6 months at $12\frac{1}{2}$% per annum is Rs 25. Find the sum.

 A) Rs.6800 B) Rs.6500 C) Rs.6000 D) Rs.6200

Explanation:

13 10353
Q:

A man wants to sell his scooter .There are two offers one at Rs12000 cash and other at a credit of Rs12880 to be paid after 8 months ,money being at 18% per annum which is better offer?

 A) Rs.12880 B) Rs.12000 C) Both are equally good D) None of the above

Explanation:

PW of Rs.12,880 due 8 months hence

= Rs[(12880 x 100)/(100+(18 x 8/12))] =Rs.11500

Clearly 12000 in cash is a better offer.

5 9601
Q:

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%

Explanation:

C.P =Rs.3000

S.P =Rs. [3600*10]/[100+(10*2)] = Rs.3000

Gain =0%

12 7032
Q:

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%

Explanation:

P.W = 2562-122 =Rs.2440

Rate = (100 x 122)/(2440 x 1/3) =15%

7 4200
Q:

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

 A) 1320 B) 1300 C) 1325 D) 1200

Explanation:

Required Sum = PW of Rs.702 due 6 months hence + PW of Rs.702 due 1 year hence

= Rs.[(100 x 702)/(100+(8 x 1/2))] + [(100 x 702)/(100+(8 x 1))]

=Rs.1325

7 4094
Q:

Find the present worth of Rs.930 due 3 years hence at 8% per annum.Aso find the discount?

 A) 186 B) 180 C) 185 D) 189

Explanation:

P.W = [(100 x Amount)/(100+(R x T))]

=[(100 x 930)/(100+(8x3))] = Rs. 750

T.D = Amount - P.W = 930 - 750 = Rs.180