Question 1

A man purchased a shirt and pant with a discount of 25% on its marked price. He sold them at a price 40% more than the price at which he bought them. How much percent the new selling price to its marked price?

Accepted Answer

Let the original price of pant and shirt be = ₹ N. ∴ Cost price of point and shirt = [N x (100 - 25)]/100 = ₹ 3N/4 And selling price of shirt and pant = (3N/4) x (100 + 40)/100 = (3N/4) x (140/100) = ₹ 21N/20 Hence, required percentage = [(21N/20 - N)/ N] x 100 % = 100 / 20 % = 5%

Question 2

By selling an article at 80 % of its marked price, a trader makes a loss of 10 %, what will be a profit percentage, if he sells it at 95 % of its marked price?

Accepted Answer

Let marked price = ₹ 100 And selling price = ₹ 80 In condition of 10% loss the cost price of article = (80 x 100)/90 = ₹ 800/9 According to the question, When SP = 95, then ∴ Required profit percentage = [{95 - (800/9)} / (800/9)] x 100 = 55/8 = 6.9% (approx)

Question 3

What is the maximum percentage discount (approximately) that a merchant can offer on his marked price, so that he ends up selling at no profit or loss, if he initially marked his goods up by 40%?

Accepted Answer

Let cost price = ₹ 100 And marked price = 100 + 40 = ₹ 140 Let required discount be R %. According to the question, 140 x (100 - R)/100 = 100 ⇒ 100 - R = (100 x 100) / 140 ∴ R = 100 - (100 x 100) / 140 = (40 x 100) / 140 = 28.5 % (approx)

Question 4

A shopkeeper allows a discount of 10% to his customers and still gains 20%, the marked price of the article which costs ₹ 450, is

Accepted Answer

Here, r = 10% and R = 20% ∴ Required per cent = (r + R)/(100 - r) x 100 % = [(10 + 20)/(100 - 10)] x 100% = (30 x 100)/90 % This shows that the marked price of the item is 100/3 % more than its cost price. ∴ Marked price of the article = (450 x 400)/300 = ₹ 600

Question 5

A dozen pair of socks quoted ₹ 80 are available at a discount of 10%. How many pair of socks can be bough for ₹ 24?

Accepted Answer

∵ MP of one dozen of pairs of socks = ₹ 80 ∴ SP of one dozen of pairs of socks =80 x (100 - 10)/100 = 80 x 90/100= ₹ 72 Hence, required number of pairs of socks purchased for ₹ 24 = (12 x 24)/72 = 4

Question 6

A retailer offers the following discount schemes for buyers on an article . i. Two successive discounts of 10 % . ii. A discount of 12 % followed by a discount of 8 %. iii. Successive discount of 15 % and 5 % . iv. A discount of 20 % . The selling p…

Accepted Answer

i. Equivalent single discount to 10 % and 10 % = 10 + 10 - (10 x 10)/100 % = 19 % ii. Equivalent single discount to 12 % and 8 % = 12 + 8 - (12 x 8)/100 = 20 - 0.96 = 19.04 % iii. Equivalent single discount to 15 % and 5 % = 15 + 5 - (15 x 5)/100 = 20 - 0.75 = 19.25 % iv. Equivalent single discount to 20 % = 20 % So, the selling price will be minimum under the scheme iv as in this scheme, the discount is maximum .

Question 7

The market price of a clock is ₹ 3200 . It is to be sold at ₹ 2448 at two successive discounts . If the first discount is 10 %, then the second discount is

Accepted Answer

Let rate of second discount = r % MP = ₹ 3200 , SP = ₹ 2448 , r1 = 10 % and r2 = r % ∴ y = MP x (100 - r1/100) (100 - r2/100) ⇒ 2448 = [3200 x (100 - 10) x (100 - r)] / (100 x 100) ⇒ (2448 x 100 x 100) / (3200 x 90) = 100 - r ∴ r = 100 - 85 = 15 %

Question 8

A shopkeeper sells not books at the rate of ₹ 457 each and earns a commission of 4% He also sells pencil boxes at the rate of ₹ 80 each and earns a commission of 20%. How much amount of commission will he he earn in two weeks, if he sells 10 noteboo…

Accepted Answer

∴ S.P of the notebook = ₹457 ∴ Commission on one notebook = ₹ (4 x 457)/100 and commission on 10 notebooks = 10 x (4 x 457)/100 = ₹ 18280 Now,S.P of the pencil box = ₹ 80 ∴ Commission on 1 pencil box = ₹ (80 x 20)/100 Commission on 6 pencil boxes = (80 x 20 x 6)/100 = ₹ 96 Hence ,total commission of 1 day = (182.80 + 96 ) = ₹ 278.80 Thus, total commission of 2 weeks = 278.80 x 14 = ₹ 3903.20

Question 9

If the price of an item is increased by 30 % and then allows two successive discounts of 10 % and 10 % . In last the price of an item is?

Accepted Answer

Let the cost price of item = ₹ N ∴ Marked price of item = N x (100 + 30)/100 = ₹ 13N/10 Selling price of the item after two successive discount = (13N/10) x[ (100 - 10)/100 x (100 - 10)/100] = (13N/10) x (90/100) x (90/100) = ₹ 1053N/1000 Increment in the price of item = [{(1053N/1000) - N} / N] x 100 % = 53/10 % = 5.3 %

Question 10

The difference between a discount of 30% on ₹ 2000 and two successive discounts of 25% and 5% on the same amount is

Accepted Answer

Single equivalent discount per cent to 25% and 5% = r1 + r2 - (r1 . r2)/100 % = 25 + 5 - (25 x 5)/100 = 30 - 1.25 = 28.78 % ∴ Required difference = [(30 - 28.75) x 2000]/100 = 1.25 x 2000/100 = ₹ 25

Question 11

A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains ₹ 56 on one item, his advertised price of the item (in ₹) is

Accepted Answer

Advertised price of the item = ₹ N ∴ Commission on advertised price of the article = ₹ (N x 23)/100 Price after commission = N - (23N/100) = ₹ 77N/100 ∴ CP of the item = [(77N/100) x 100]/(100 + 10) = 77N/110 = ₹ 7N/10 Profit = 77N/100 - 7N/10 = ₹ 7N/100 ⇒ 56 = 7N/100 ∴ N = (56 x 100)/7 = ₹ 800

Question 12

A shopkeeper allows a discount of 4% on his article. If cost price of the article is ₹ 100 and he wants to get a profit of 20%. Then, its marked price will be

Accepted Answer

∵ Cost price of article = ₹ 100 ∴ Selling price of the article for 20% profit = 100 x (100 + 20)/100 = ₹ 120 Hence, marked price of the article for 4% discount = 120 x 100/(100 - 4) = 120 x 100/96 = ₹ 125

Question 13

A merchant purchases a wrist watch for ₹ 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then, the list price of the watch is

Accepted Answer

CP of watch = ₹ 450 SP of watch = 450 x [(100 + 20)/100] = ₹ 540 ∴ List price of watch = (540 x 100) / (100 - 10) = ₹ 600

Question 14

In order that there may be a profit of 20% after allowing a discount of 10% on the marked price, the cost price of an article has to be increased by

Accepted Answer

Let MP = ₹ N ∴ SP = N x (100 - 10)/100 = ₹ 9N/10 ∴ CP = (9N/10) x [100/(100 + 20)] = ₹ 3N/4 Thus, CP has to be increased by = [(N - 3N/4) / (3N/4)] x 100% = [(N/4) / (3N/4)] x 100 % = 331/3 %

Question 15

The cost price of an article is 64% of the marked price. The gain percentage after allowing a discount of 12% on the marked price is

Accepted Answer

Let MP of the article = ₹ N ∴ C P of the article = (N x 64) / 100 = ₹ 16N/25 And SP of the article = [N x (100 - 12)]/100 = ₹ (N x 22)/25 ⇒ profit = [ 22N/25 - 16N/25 ] = ₹ 6N/25 Hence, profit per cent = [(6N/25) / (16N/25)] x 100% = (6 x 100)/16 = 37.5%

Question 16

If a commission of 10% is given on the written price of an article, the gain is 20%. The gain per cent, when the commission is increased to 20%, will be?

Accepted Answer

Let MP of the article = ₹ N ∴ SP of the article = N x (100 - 10)/100 = ₹ 9N/10 ⇒ CP of the article = [(9N/10) x 100]/(100 + 20) = (9N x 10)/120 = ₹ 3N/4 Now, new SP of the article = [N x (100 - 20)]/100 = ₹ 4N/5 New profit = 4N/5 - 3N/4 = (16N - 15N)/20 = ₹ N/20 Hence, profit per cent = [(N/20) / (3N/4)] x 100 % = (4 x 100)/(3 x 20) % = 62/3%

Question 17

If the discount on a certain sum in 2 years at a certain rate is $ 150 and the interest in 3 years is $ 240. Find the sum and the rate of interest.

Accepted Answer

Question 18

A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :

Accepted Answer

Question 19

Find the present worth ( P.W.) and the true discount reckoning 6 % per annum simple interest of $ 176 due in 20 months time.

Accepted Answer

Question 20

The discount on $ 5229 due in 1 year 9 months reckoning compound interest at 5 % is :

Accepted Answer

Discount Questions