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.



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




4. (S.I) - (T.D )= S.I on T.D

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


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


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

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16 11298

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



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11 10033

The difference between Simple Interest and True Discount on a certain sum of money for 6 months at % 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


Let amount be Rs.x

T.D = \inline \fn_jvn \frac{x\times \frac{25}{2}\times \frac{1}{2}}{100+\left ( \frac{25}{2}\times \frac{1}{2} \right )}  =\inline \fn_jvn \frac{x}{17} 

S.I = \inline \fn_jvn \frac{x\times \frac{25}{2}\times \frac{1}{2}}{100} =\inline \fn_jvn \frac{x}{16}

\fn_jvn \therefore  \fn_jvn \frac{x}{16}-\frac{x}{17}=25  \fn_jvn \Rightarrow  \inline \fn_jvn 17x-16x=25\times 16\times 17  \inline \fn_jvn \Rightarrow \inline \fn_jvn x=6800

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13 9867

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
Answer & Explanation Answer: B) Rs.12000


PW of Rs.12,880 due 8 months hence

        = Rs\inline \fn_jvn \left [ \left ( \frac{12880\times 100}{100+(18\times \frac{8}{12})} \right ) \right ] =Rs.11500

Clearly 12000 in cash is a better offer.

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5 9288

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%


C.P =Rs.3000

S.P =\inline {\color{Black}Rs.[\frac{3600\times 100}{100+(10\times 2)}]=Rs.3000}

Gain =0%

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11 6718