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 True Discount Questions

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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. P.W=100×Amount100+R×T=100×T.DR×T

 

2. T.D=P.W×R×T100=Amount×R×T100+R×T

 

3.  Sum=S.I×T.DS.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=Amount1+R100T

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
 
Answer & Explanation Answer: 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) x 600] / 100 = Rs.750

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56 36704
Q:

The difference between Simple Interest and True Discount on a certain sum of money for 6 months at 1212% per annum is Rs 25. Find the sum.

A) Rs.6800 B) Rs.6500
C) Rs.6000 D) Rs.6200
 
Answer & Explanation Answer: A) Rs.6800

Explanation:

 

 

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53 19572
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%
 
Answer & Explanation Answer: A) 0%

Explanation:

C.P = Rs.3000 

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

Gain =0%

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35 25412
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
 
Answer & Explanation Answer: B) gains Rs. 50

Explanation:

ke

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28 30422
Q:

What is the true discount on a bill of Rs.2916 due in 3 years hence at 8% C.I.?

A) Rs.600 B) Rs.601
C) Rs.602 D) Rs.603
 
Answer & Explanation Answer: C) Rs.602

Explanation:

PW = Amount1+R100T 

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27 4698
Q:

The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.

A) rs.1175 B) rs.1375
C) rs.1475 D) rs.1575
 
Answer & Explanation Answer: B) rs.1375

Explanation:

PW = 100×Amount100+R×T 

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26 5216
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
 
Answer & Explanation Answer: B) 180

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

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20 13181
Q:

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?

A) Rs.948 B) Rs.876
C) Rs.768 D) Rs.658
 
Answer & Explanation Answer: C) Rs.768

Explanation:

P.W. = 100×T.DR×T = 100×16814×2 = 600.

Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.

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