True Discount(Quantitative Aptitude > Discount ) Questions and answers for exam Preparation

Question 1. A shopkeeper offers 10% discount on the marked price of his articles and still makes a profit of 20%. What is the actual cost of the article marked Rs.500 for him ?

Rs.375
Rs.400
Rs.440
Rs.425

Explanation:-

Answer: Option A. -> Rs.375
Answer: (a)Let the cost price of article be x$500 × 90/100 = 120/100 × x$450 = ${6x}/5$$x = {450 × 5}/6$ = Rs.375Using Rule 6,C.P. = ? , M.P. = Rs.500, r = 20%, D = 10%$\text"MP"/\text"CP" = {100 + r}/{100 - D}$$500/\text"CP" = {100 + 20}/{100 - 10}$C.P.= ${500 × 90}/120$ = Rs.375

Question 2. The price that Akbar should mark on a pair of shoes which costs him Rs.1,200 to gain 12% after allowing a discount of 16% (in rupees) is

1,500
1,600
1,344
1,433

Explanation:-

Answer: Option B. -> 1,600
Answer: (b)Let the marked price be x.$x × 84/100 = {1200 × 112}/100$$x × 84/100 = 112 × 12$$x = {112 × 1200}/84$ = Rs.1600Using Rule 6,C.P. = Rs.1200, r = 12%, D = 16%$\text"MP"/\text"CP" = {100 + r}/{100 - D}$$\text"MP"/1200 = {100 + 12}/{100 - 16}$M.P.= ${112 × 1200}/84$ = Rs.1600

Question 3. In order to maintain the price line a trader allows a discount of 10% on the marked price of an article. However, he still makes a profit of 17% on the cost price. Had he sold the article at the marked price, he would have earned a profit per cent of

35%
33%
30%
32%

Explanation:-

Answer: Option C. -> 30%
Answer: (c)Let the marked price be Rs.100.S.P. = 90% of 100 = Rs.90Profit = 17%C.P. = Rs.$90 × 100/117$ = Rs.$1000/13$If no discount is allowed,S.P. = Rs.100Profit = Rs.$(100 - 1000/13)$ = Rs.$300/13$Profit % = ${300/13}/{1000/13}$ × 100 = 30%Using Rule 6,Here, D = 10%, r = 17%,Let the M.P. = Rs.100$\text"MP"/\text"CP" = {100 + r}/{100 - D}$$100/\text"CP" = {100 + 17}/{100 - 10}$$100/\text"C.P." = 117/90$C.P. = ${100 × 90}/117 = 1000/13$Profit = S.P. - C.P.= $100 - 1000/13$ = Rs.$300/13$Profit % = ${300/13}/{1000/13} × 100%$ = 30%

Question 4. A manufacturer marked an article at Rs.50 and sold it allowing 20% discount. If his profit was 25%, then the cost price of the article was

Rs.30
Rs.32
Rs.40
Rs.35

Explanation:-

Answer: Option B. -> Rs.32
Answer: (b)Marked price = Rs.50S.P. after discount = 80% of 50 = Rs.40If the CP of article be x, then${125 × x}/100 = 40$$x = {40 × 100}/125$ = Rs.32Using Rule 6,Here, M.P. = Rs.50, C.P. = ?,r = 25%, D = 20%$\text"MP"/\text"CP" = {100 + r}/{100 - D}$$50/\text"CP" = {100 + 25}/{100 - 20}$C.P.= ${50 × 80}/125$ = Rs.32

Question 5. A shopkeeper marks his goods 40% above the cost price. He allows a discount of 5% for cash payment to his customers. He receives Rs.1064 after paying the discount. His profit is

Rs.800
Rs.200
Rs.264
Rs.164

Explanation:-

Answer: Option A. -> Rs.800
Answer: (a)Cost price of article = Rs.x$x × 140/100 × 95/100 = 1064$$x = {1064 × 100 × 100}/{140 × 95}$ = Rs.800

Question 6. An article listed at Rs.800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price ?

Rs.680
Rs.640
Rs.620
Rs.600

Explanation:-

Answer: Option A. -> Rs.680
Answer: (a)Using Rule 5,Effective discount= 25 + 15 - ${25 × 15}/100$= 40 - 3.75 = 36.25 %CP for buyer= (100 - 36.25) % of 800= ${63.75 × 800}/100$ = Rs.510To gain 20%,SP = Rs.$({120 × 510}/100)$ = Rs.612Let the list price be Rs.x.90% of x = Rs.612${90x}/100$ = 612$x = 61200/90$ = Rs.680

Question 7. The marked price of a T.V. is Rs.16,000. After two successive discounts it is sold for Rs.11,400. If the first discount is 5%, then the rate of second discount is

25%
30%
15%
20%

Explanation:-

Answer: Option A. -> 25%
Answer: (a)After a discount of 5%SP = ${95 × 16000}/100$ = Rs.15200Let the second discount be x%.x% of 15200 = (15200 - 11400)${x × 15200}/100 = 3800$$x = {3800 × 100}/15200 = 25$Second discount = 25%Using Rule 3,Here, M.P. = 16000, S.P. = 11400, $D_1 = 5%, D_2$ = ?S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$11400 = 16000$({100 - 5}/100)({100 - D_2}/100)$$114000/{16 × 95} = 100 - D_2$$75 = 100 - D_2 ⇒ D_2$ = 25%

Question 8. An article is listed at Rs.900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single discount of 16%, instead of two discounts ?

Loss of Rs.4.76
Gain of Rs.5.76
Gain of Rs.4.76
Loss of Rs.5.76

Explanation:-

Answer: Option D. -> Loss of Rs.5.76
Answer: (d)Using Rule 5,Equivalent discount for two successive discounts of 8% and 8%= $(8 + 8 - {8 × 8}/100)$%= (16–0.64) % = 15.36 %SP = (100 –15.36) % of 900= Rs.$({84.64 × 900}/100)$ = Rs.761.76For a single discount of 16%,SP = 84% of 900= Rs.$({84 × 900}/100)$ = Rs.756Certainly seller will lose in this case.Loss = Rs. (761.76 - 756) = Rs.5.76

Question 9. The marked price of watch was Rs.820. A man bought the watch for Rs.570.72 after getting two successive discounts, of which the first was 20%. The second discount was

11%
13%
18%
15%

Explanation:-

Answer: Option B. -> 13%
Answer: (b)Total discount=Rs.(820 - 570.72) = Rs.249.28First discount = $820 × 20/100$ = Rs.164Second discount= Rs.(249.28 - 164) = Rs.85.28Price of the article after first discount= Rs.(820 - 164) = Rs.656If the second discount be x% , thenx% of 656 = 85.28$x = {85.28 × 100}/656 = 13%$Using Rule 3,Here, M.P. = Rs.820, S.P. = 570.72, $D_1 = 20%, D_2$ = ?S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$$570.72 = 820 ({100 - 20}/100)({100 - D_2}/100)$$5707200/{820 × 80} = 100 - D_2$$100 - D_2 = 87 ⇒ D_2$ = 13%

Question 10. A shopkeeper gives two successive discounts on an article marked Rs.450. The first discount given is 10 per cent. If the customer pays Rs.344.25 for the article, the second discount given is

15 per cent
12 per cent
14 per cent
10 per cent

Explanation:-

Answer: Option A. -> 15 per cent
Answer: (a) Let the second discount be x per cent.According to the question,$450 × {100 - 10}/100 × {100 - x}/100$ = 344.25100 - x = ${344.25 × 100 × 100}/{450 × 90}$100 - x = 85x = 100 - 85 = 15%.Using Rule 3,Here, M.P. = Rs.450, S.P. = Rs.344.25, $D_1 = 10%, D_2$ = ?S.P. = M.P.$({100 - D_1}/100)({100 - D_2}/100)$$344.25 = 450 × ({100 - 10}/100)({100 - D_2}/100)$$3442500/{450 × 90} = (100 - D_2)$$85 = 100 - D_2 ⇒ D_2$ = 15%