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Home > Practice > Arithmetic Aptitude > True Discount > Miscellaneous

11. 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?

A. Rs. 10

B. Rs. 10.40

C. Rs. 15.20

D. Rs. 13

Discuss

Solution:

S.I. on Rs. (260 - 20) for a given time = Rs. 20
S.I. on Rs. 240 for half time = Rs. 10
T.D. on Rs. 250 = Rs. 10
∴ T.D. on Rs. 260
= Rs.

\frac{10}{250}

× 260
= Rs. 10.40

12. The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:

A. 12%

B. 14%

C. 15%

D. 16%

Discuss

Solution:

S.I. on Rs. 750 = T.D. on Rs. 960
This means P.W. of Rs. 960 due 2 years hence is Rs. 750
∴ T.D. = Rs. (960 - 750) = Rs. 210
Thus, S.I. on R.s 750 for 2 years is Rs. 210

\begin{aligned} ∴ Rate = (\frac{100 \times 210}{750 \times 2}) % \\ = 14 % \end{aligned}

13. 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:

A. Rs. 1800

B. Rs. 1450

C. Rs. 1360

D. Rs. 6800

Discuss

Solution:

\begin{aligned} Sum = \frac{S . I . \times T . D .}{S . I . - T . D .} \\ = \frac{85 \times 80}{85 - 80} \\ = R s . 1360 \end{aligned}

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

A. Rs. 1325

B. Rs. 1300

C. Rs. 1350

D. Rs. 1500

Discuss

Solution:

Required sum
= P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence

\begin{aligned} = R s . [\frac{100 \times 702}{100 + 8 \times \frac{1}{2}} + \frac{100 \times 702}{100 + (8 \times 1)}] \\ = R s . (675 + 650) \\ = R s . 1325 \end{aligned}

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

A. Rs. 768

B. Rs. 968

C. Rs. 1960

D. Rs. 2400

Discuss

Solution:

\begin{aligned} P . W . = \frac{100 \times T . D .}{R \times T} \\ = \frac{100 \times 168}{14 \times 2} \\ = 600 \\ ∴ Sum = (P . W . + T . D .) \\ = R s . (600 + 168) \\ = R s . 768 \end{aligned}

16. A tradesman marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. How much profit or loss does he make, if any ?

A. 1% gain

B. 1% loss

C. 5% gain

D. No gain no loss

Discuss

Solution:

Let cost price of goods = Rs 100
Market price of goods

\begin{aligned} = 110 % of 100 \\ = \frac{110}{100} \times 100 \\ =  Rs . 110 \end{aligned}

After discount selling price of goods

\begin{aligned} = 90 % of 110 \\ = \frac{90}{100} \times 110 \\ = Rs . 99 \end{aligned}

Loss = 100 - 99 = Rs. 1

\begin{aligned} Loss % = \frac{1}{100} \times 100 \\ = 1 % \end{aligned}

Alternate :

\begin{aligned} Loss % = \frac{x \times y}{100} % \\ Loss % = \frac{10 \times 10}{100} \\ = 1 % \end{aligned}

17. A discount of $2 \frac{1}{2} %$ is given to the customer on the marked price of an article. A man bought the article for Rs 39. The marked price of the article is = ?

A. Rs. 42

B. Rs. 36.50

C. Rs. 40

D. Rs. 41.50

Discuss

Solution:

Discount = 2.5%

= \frac{2.5}{100} = \frac{1}{40} \begin{matrix} \to Discount \\ \to Market Price \end{matrix}

Market Price = Rs. 40
Discount = Rs. 1
Cost Price = 40 - 1 = Rs. 39
39 → 39 Actual Cost Price
40 → Rs. 40

18. The marked price of a watch was Rs. 720. A man bought the same for Rs. 550.80, after getting two successive discounts, the first 10%. What was the second discount rate ?

A. 12%

B. 14%

C. 15%

D. 18%

Discuss

Solution:

Market price of a watch = Rs. 720
After 1^st discount

\begin{aligned} =  90 % of 720 \\ = \frac{90}{100} \times 720 \\ = Rs . 648 \end{aligned}

Cost price of watch = Rs. 550.80
Difference
= 648 - 550.80
= Rs. 97.20

\begin{aligned} 2^{nd} discount \\ = \frac{97.20}{648} \times 100 \\ = \frac{9720}{648} \\ = 15 % \end{aligned}

19. A shopkeeper marks his goods 20% above cost price, but allows 30% discount for cash payment. His net loss is ?

A. 8%

B. 10%

C. 16%

D. 20%

Discuss

Solution:

Let the cost price of goods = Rs. 100
Market price of goods

\begin{aligned} =  120 % of 100 \\ = \frac{120}{100} \times 100 \\ =  Rs . 120 \end{aligned}

After discount selling price of goods
= 70% of 120
= Rs. 84

\begin{aligned} Loss  =  100 - 84 = Rs .16 \\ Loss % = \frac{16}{100} \times 100 = 16 % \end{aligned}

Alternate :

\begin{aligned} Formula  = x \pm y \pm \frac{x \times y}{100} \\ Loss % =  20 - 30 - \frac{20 \times 30}{100} \\ = - 10 - 6 \\ = - 16 % (Loss) \end{aligned}

20. The equivalent single discount for two successive discounts of 15% and 10% is = ?

A. 25%

B. 20%

C. 23.5%

D. 20.85%

Discuss

Solution:

Equivalent to a single discount

\begin{aligned} = 15 + 10 - \frac{15 \times 10}{100} \\ = 25 - 1.5 \\ = 23.5 % \end{aligned}

Alternate :

\begin{aligned} Market price  =  Rs .100 \\ Cost price \\ =  100 \times \frac{85}{100} \times \frac{90}{100} \\ =  Rs . 76.5 \\ Difference  = 100 - 76.5 \\ = 23.5 \\ Difference % \\ = \frac{23.5}{100} \times 100 \\ = 23.5 % \end{aligned}

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