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Home > Practice > Arithmetic Aptitude > True Discount > Miscellaneous

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%

Discuss

Solution:

\begin{aligned} C .P . = R s . 3000 \\ S .P . = R s . [\frac{3600 \times 100}{100 + (10 \times 2)}] \\ = R s . 3000 \\ Gain = 0 % \end{aligned}

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%

Discuss

Solution:

\begin{aligned} P .W . = R s . (2562 - 122) \\ = R s .2440 \\ ∴ S .I . on Rs . 2440 for 4 months is Rs . 122 . \\ ∴ Rate = [\frac{100 \times 122}{2440 \times \frac{1}{3}}] % = 15 % \end{aligned}

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. Rs. 9025.20

B. Rs. 9200

C. Rs. 9600

D. Rs. 9560

Discuss

Solution:

\begin{aligned} Required Money \\ = P .W . of Rs . 10028 due 9 months hence \\ = R s . [\frac{10028 \times 100}{100 + (12 \times \frac{9}{12})}] \\ = R s . 9200 \end{aligned}

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. Rs. 12,000 in cash

B. Rs. 12,880 at credit

C. Both are equally good

D. Rs. 18.33

Discuss

Solution:

\begin{aligned} = P .W . of Rs . 12,880 due 8 months hence \\ = R s . [\frac{12880 \times 100}{100 + (18 \times \frac{8}{12})}] \\ = R s . (\frac{12880 \times 100}{112}) \\ = R s . 11500 \end{aligned}

Clearly 12000 in cash is a better offer.

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. Rs. 20

B. Rs. 21.81

C. Rs. 22

D. Rs. 18.33

Discuss

Solution:

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.

\begin{aligned} T .D . on Rs . 110 \\ = R s . (\frac{20}{120} \times 110) \\ = R s . 18.33 \end{aligned}

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. $16 \frac{2}{3}$ %

B. $14 \frac{1}{2}$ %

C. $13 \frac{1}{3}$ %

D. 15%

Discuss

Solution:

\begin{aligned} S .P . = 102 % o f R s . 600 \\ = \frac{102}{100} \times 600 \\ = R s . 612 \\ Now, \\ P .W . = Rs . 612 and sum = R s . 688.50 \\ ∴ T .D . = R s . (688.50 - 612) \\ = R s . 76.50. \\ Thus, S .I . on Rs . 612 for 9 months is Rs . 76 .50 . \\ ∴ Rate = (\frac{100 \times 76.50}{612 \times \frac{3}{4}}) % \\ = 16 \frac{2}{3} % \end{aligned}

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. Rs. 1386

B. Rs. 1764

C. Rs. 1575

D. Rs. 2268

Discuss

Solution:

\begin{aligned} Let P .W . be Rs . x . \\ Then, S .I . on Rs . x at 16 % for 9 months \\ = R s . 189 \\ ∴ x \times 16 \times \frac{9}{12} \times \frac{1}{100} \\ = 189 o r x = 1575. \\ ∴ P . W . = R s . 1575. \\ ∴ Sum due = P . W . + T . D . \\ = R s . (1575 + 189) \\ = R s . 1764 \end{aligned}

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. loses Rs. 30

D. gains Rs. 30

Discuss

Solution:

\begin{aligned} S .P . = P .W . of Rs . 2200 due 1 year hence \\ = R s . [\frac{2200 \times 100}{100 + (10 \times 1)}] \\ = R s . 2000 \\ ∴ Gain = R s . (2000 - 1950) \\ = R s . 50 \end{aligned}

9. 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:

A. 6 months

B. 8 months

C. 9 months

D. 10 months

Discuss

Solution:

\begin{aligned} P . W . = R s . (1760 - 160) = R s . 1600 \\ ∴ S .I . on Rs . 1600 at 12 % is Rs . 160 \\ ∴ Time = \frac{100 \times 160}{1600 \times 12} \\ = \frac{5}{6} years \\ = (\frac{5}{6} \times 12) months \\ = 10 months \end{aligned}

10. The present worth of Rs. 2310 due $2 \frac{1}{2}$ years hence, the rate of interest being 15% per annum, is:

A. Rs. 1750

B. Rs. 1680

C. Rs. 1840

D. Rs. 1443.75

Discuss

Solution:

\begin{aligned} P . W . = R s . [\frac{100 \times 2310}{100 + (15 \times \frac{5}{2})}] \\ = R s . 1680 \end{aligned}

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