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Profit and Loss - Quantitative Aptitude - Aptitude question and answers
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Profit and Loss

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  • Cost Price: The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
  • Selling Price: The price, at which an article is sold is called its selling prices, abbreviated as S.P.
  • Profit or Gain: If S.P. is greater than C.P., the seller is said to have a profit or gain.
  • Loss: If S.P. is less than C.P., the seller is said to have incurred a loss
  • Gain = (S.P.) – (C.P.)
  • Loss = (C.P.) – (S.P.)
  • Loss or gain is always reckoned on C.P.
  • Gain Percentage: (Gain %) => Gain % = (Gain x 100 / C.P)
  • Loss Percentage: (Loss %) => Loss % = (Loss x 100 / C.P)
  • Selling Price: (S.P.) => SP = [(100 + Gain %) / 100 x C.P]
  • Selling Price: (S.P.) => SP =[(100 – Loss %) / 100 x C.P]
  • Cost Price: (C.P.) => C.P = [100 /(100 + Gain %) x S.P]
  • Cost Price: (C.P.) => C.P = [100 / (100 – Loss %) x S.P]
  • If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.
  • If an article is sold at a loss of say, 35% then S.P. = 65% of C.P.
  • When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by: % Loss (Common Loss and Gain % / 10)2 = (x / 10)2
  • If a trader professes to sell his goods at cost price, but uses false weights, then % Gain = [Error / (True Value) – (Error) x 100]%

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Profit and loss - Question and Answers

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Question 1
The ratio of the cost price and the selling price is 4:5. The profit percent is?
A
10
B
20
C
25
D
30
Question 1 Explanation: 
profit is always calculated on cost price
so, C.P = 4 , S.P = 5
Profit=S.P - C.P, 5 - 4 = 1
profit % = profit / cost price * 100 then, 1 / 4 * 100 = 25
Question 2
If on selling 12 notebooks a seller makes a profit equal to selling price of 4 notebook, what is his profits percentage?
A
16
B
25
C
50
D
None of these
Question 2 Explanation: 
If there is profit on selling item = selling price of an article
To find profit %, simply minus 12 from 4 = 8
Profit % = 4/8 * 100 = 50
Question 3
A vender loses the selling price of 4 oranges on selling 36 oranges his loss percentage is?
A
10
B
11
C
12
D
None of these
Question 3 Explanation: 
If there is loss on selling item = selling price of an article
To find loss%, simply add 36 to 4 = 40
Loss % = 4/40 * 100 = 10
Question 4
A vender by selling 12 toffee for a rupee. A man loses 20%. How many for a rupee should he sell to get a gain of 20%?
A
10
B
20
C
8
D
12
Question 4 Explanation: 
12 toffee for rs 1 loss 20% then
C.P = 1 * 100/80 = 5/4 on this price we have to gain profit of 20%
So, 5/4 * 120/100 = 3/2
If for Rs. 2/3 we have 12 toffee then for rs 1 we have
= 12 x 2/3
= 8
Question 5
A sell a bicycle of to B at a profit of 20%. B sell it to C at profit of 25%. If C pays rs. 225 for it, the cost price of the bicycle for A is?
A
110
B
120
C
125
D
150
Question 5 Explanation: 
125% of 120% of A = 225
=> 125/100 * 120/100 * A = 225
=> A = (225 * 2/3)
A = 150
Question 6
A shopkeeper professes to sell his goods at cost price but uses a weight of 800gm instead of 1kg. Thus he makes a profit of?
A
20%
B
16%
C
25%
D
50%
Question 6 Explanation: 
The shopkeeper uses weight of 800gm instead of 1kg
So, 200gm difference = profit
profit % = 200/800 * 100 = 25%
Question 7
A shopkeeper cheats to the extents of 10% while buying as well as selling by using false weight his total gain is?    
A
10%
B
11%
C
20%
D
21%
Question 7 Explanation: 
A shopkeeper cheats to the extents of 10% while buying as well as selling
(100 - 110 = 10% on selling)
(110 - 121 = 10% on buying)
Hence difference = 21 = Profit
Question 8
An article when sold at a gain of 5% yields rs. 15 more than when sold at a loss of 5%. Its cost price would be?
A
150
B
200
C
250
D
300
Question 8 Explanation: 
Difference between gain% and loss% equal to 10%
then, 10% = rs. 15
100% = rs. 150 , that is your cost price
Question 9
The price of an article has been reduced by 25%. In order to restore the original price the reduced price must be increased by?
A
25%
B
30%
C
33%
D
33.1/3%
Question 9 Explanation: 
Reduced price = (100 - 75) = 25%
Original price = 25/75 * 100 = 33.1/3%
Question 10
An article was sold at 16% gain. Had it been sold for rs. 200 more, the gain would have been 20% then the cost price of the article is?
A
5000
B
4800
C
4500
D
5200
Question 10 Explanation: 
Difference in gain % equal to 200,
Then 20% - 16% = 4%
4% = 200 then,
100% = 5000 that is your cost price of the article
Question 11
A toy sells for 6.00 at a profit of 25% of the selling price. Separate this selling price into cost and profit?
A
cost = 3.75, profit = 1.87
B
cost = 4.50, profit = 1.50
C
cost = 3.40, profit = 2.50
D
cost = 5.50, profit = 4.50
Question 11 Explanation: 
Selling price x % profit = profit
Selling price = profit = cost
6.00 x 0.25 = 1.50, profit
6.00 – 1.50 = 4.50, cost
Question 12
At a sale, necklace selling at 50.00 are sold at a loss of 60% of selling price. What is the loss and the original cost?
A
Loss = 34.00, Cost = 20.00
B
Loss = 44.00, Cost = 10.00
C
Loss = 40.00, Cost = 30.00
D
Loss = 30.00, Cost = 20.00
Question 12 Explanation: 
Selling price x % loss = loss
Selling price + loss = cost
50.00 x .60 = 30.00, loss
50.00 – 30.00 = 20.00, cost
Note: To find the loss and the cost when the selling price and the percent loss are given, multiply the selling price by the percent loss and subtract the result from the selling price
Question 13
Socks that cost 7.00 per pair were sold at a loss of 25% of selling price. What was the selling price?
A
8.12
B
3.20
C
5.60
D
4.60
Question 13 Explanation: 
Cost / ( 100% + %loss ) = selling price
7.00 / 1.25 = 5.60, selling price
Note:To find the selling price when the cost and the percent loss are given, add the percent loss to 100% and divide the cost by this sum
Question 14
A kind of tape is selling at a profit of 12% of selling price, equal to 18 per yard. What is the selling price of the tape?  
A
1.00
B
1.50
C
1.60
D
2.40
Question 14 Explanation: 
Profit / profit% = selling price
18 /.12 = 1.50 selling price
Note:To find the selling price when the profit and the percent profit are given, or to find the selling price when the loss and the percent loss are given, divide the profit or loss by the percent profit or loss
Question 15
A candy bar sells for 1.30 at a profit of 65. What percent of profit on selling price does this represent?
A
60%
B
20%
C
30%
D
50%
Question 15 Explanation: 
Gain / selling price = % profit
65 / 1.30 = .5 or 50% profit
Note: To find the percent profit or loss, divide the amount gained or lost by the selling price
Question 16
20% loss on cost is what percent loss on selling price?
A
25%
B
27%
C
39%
D
40%
Question 16 Explanation: 
% loss on cost / ( 100% – % loss on cost ) = % loss on selling price
0.20 / 80 = .0025 or 25% loss on selling price
Note: To reduce percent loss on cost to percent loss on selling price, divide percent loss on cost by 100% minus percent loss on cost.
Question 17
20% loss on selling price is what percent loss on cost?
A
.15
B
.12
C
.17
D
.16
Question 17 Explanation: 
% loss on selling price / ( 100% + % loss on selling price ) = % loss on cost
.20 / 1.20 = .16666 or .16.67% loss on cost
Note: To reduce percent loss on selling price to percent loss on cost, divide percent loss on selling price by 100% plus percent loss on selling price.
Question 18
A coat marked up 60% carries what percent of profit on selling price?  
A
24.5%
B
27.3%
C
37.5%
D
42.3%
Question 18 Explanation: 
% profit on cost / ( 100% + % profit on cost ) = % profit on selling price
.60 / 1.60 = .375 or 37.5% on selling price
Note: To reduce percent mark-up (percent profit on cost) to percent profit on selling price, divide percent mark-up by 100% plus percent mark-up
Question 19
The cost price of 40 articles is the same as the selling price of 25 articles. Find the gain percent?
A
65%
B
60%
C
15%
D
75%
Question 19 Explanation: 
Grade Stack methods
From given Expression We take x = 40 , y = 25
Then Gain % = (x - y) x 100 / y
Gain per cent = (40 - 25)/25 × 100 = 15/25 × 100 = 60%
Question 20
Bananas are bought at the rate of 6 for Rs. 5 and sold at the rate of 5 for Rs. 6. Profit percent is?
A
36%
B
42%
C
44%
D
48%
Question 20 Explanation: 
To avoid fraction, let the number of bananas bought LCM of 5 and 6 = 30
CP of 30 bananas = 5 x 5 = Rs. 25
SP of 30 Bananas = 6 x 6 = Rs. 36
Profit = Rs. (36 - 25) = Rs. 11
Profit % = 11/25 × 100 = 44%
Question 21
A man bought oranges at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs. 57. How many oranges should be sold to earn a net profit of Rs 45?
A
90
B
100
C
135
D
150
Question 21 Explanation: 
Let the man buy 24 (LCM of 8 and 12) oranges
C.P. of 24 oranges = 34/8 × 24 = Rs. 102
S.P. of 24 oranges = 27/12 × 24 = Rs. 114
Gain = 114 – 102 = Rs. 12
Rs. 12 = 24 oranges
Rs. 45 = 24/12 × 45 = 90 oranges
Question 22
A shopkeeper earns a profit of 12% on selling a book at 10% discount on printed price. The ratio of the cost price to printed price of the book is?  
A
45 : 56
B
50:61
C
90:97
D
99:125
Question 22 Explanation: 
C.P. of the book = Rs.x
Printed price = Rs. y
(y * 90)/100=x * 112/100
x/y = 90/112 = 45/56
Question 23
A dealer sold two types of goods for Rs 10,000 each. On one of them, he lost 20% and on the other he gained 20%. His gain or loss per cent in the entire transaction was?
A
2% loss
B
2% gain
C
4% gain
D
4% loss
Question 23 Explanation: 
Here, S.P. is same, Hence there is always a loss
Loss percent = (20 × 20)/100 = 4%
Question 24
On selling an article for Rs.170, a shopkeeper loses 15%. In order to gain 20%, he must sell that article at rupees?
A
215.50
B
212.50
C
240
D
210
Question 24 Explanation: 
C.P. of article = (200 × 120) / 100 = Rs. 240
Question 25
An article is sold at a loss of 10%. Had it been sold for Rs. 9 more, there would have been a gain of 12 1/2% on it. The cost price of the article is?
A
Rs. 40
B
Rs. 45
C
Rs. 50
D
Rs. 35
Question 25 Explanation: 
Let the cost price of the article = Rs. x
S.P. at 10% loss = x * 90/100 = Rs. 9x
S.P. at 12 1/2 % gain
x * (100+12.1/2)/100 = Rs. 225x / 200
According to the question, 9x + 9 = 225x / 200
180x + 1800 = 225x
x = Rs. 40
Question 26
A sells a suitcase to B at 10% profit. B sells it to C at 30% profit. If C pays Rs 2860 for it, then the price at which A bought is?  
A
1000
B
1600
C
2000
D
2500
Question 26 Explanation: 
If the C.P. of suitcase for A be Rs. x, then
x * 110/100 * 130/100 = 2860
x = (2860 * 100 * 100) / (110 * 130) = Rs. 2000
Question 27
Arun marks up the computer he is selling by 20% profit and sells them at a discount of 15%. Arun’s net gain percent is?
A
4
B
2
C
3.5
D
2.5
Question 27 Explanation: 
Gradestack method: r1 = 20 , r2 = 15
Formula =[(r1 – r2) – (r1 x r2) /100]
[(20 - 15) - (20 × 15) /100]
= 20 - 18
= 2%
Question 28
A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was?
A
Rs. 200
B
Rs. 25
C
Rs. 400
D
Rs. 250
Question 28 Explanation: 
Let the C.P. of article be Rs. x
105% of x – 80% of x = Rs. 100
25% of x = Rs. 100
x = Rs. (100 × 100) / 25
x = Rs. 400
Question 29
A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent?
A
1%
B
2%
C
3%
D
4%
Question 29 Explanation: 
So we have C.P = 27.50
S.P. = 28.60
Gain = 28.60 - 27.50 = Rs. 1.10
Gain%=(GainCost ∗ 100)% = (1.1027.50 ∗ 100)% = 4%
Question 30

A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the lost percent?

A
10%
B
20%
C
25%
D
28%
Question 30 Explanation: 
We know, C.P. = 5000
S.P. = 4000
Loss = 5000 - 4000 = 1000
Loss% = (Loss Cost ∗ 100)% = (10005000 ∗ 100)% = 20%
Question 31
A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit?
A
Rs.1200
B
Rs. 1230
C
Rs. 1260
D
Rs. 1290
Question 31 Explanation: 
Let the new S.P. be x, then
(100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(951140=105x)
=> x=1260
Question 32
A book was sold for Rs 27.50 with a profit of 10%. If it were sold for Rs. 25.75, then would have been percentage of profit and loss?
A
2% Profit
B
3% Profit
C
2% Loss
D
3% Loss
Question 32 Explanation: 
S.P.=(100 + gain% 100 ∗ C.P)
So, C.P. = (100110 ∗ 25.75)When S.P. = 25.75 then
Profit=25.75 − 25 = Re.0.75
Profit%=0.7525 ∗ 100=3%
S.P. = (100 + gain%100 ∗ C.P)So,
C.P. = (100110 ∗ 25.75)When S.P. = 25.75 then Profit = 25.75 − 25=Re.0.75
Profit%=0.7525 ∗ 100 = 3%
Question 33
If the cost price is 25% of selling price. Then what is the profit percent?
A
150%
B
200%
C
300%
D
350%
Question 33 Explanation: 

Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = 75/25 * 100 = 300

Question 34
A pair of articles was bought for Rs. 37.40 at a discount of 15%. What must be the marked price of each of the articles?  
A
Rs 15
B
Rs 20
C
Rs 22
D
Rs 25
Question 34 Explanation: 
So rate of One article = 37.40 / 2 = Rs. 18.70
Let Marked price = Rs X
then 85% of X = 18.70
=> X = 1870 / 85 = 22
Question 35
A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is?
A
18%
B
20%
C
22%
D
24%
Question 35 Explanation: 
Let the cost price = Rs 100
then, Marked price = Rs 135
Required gain = 8%,
So Selling price = Rs 108
Discount = 135 - 108 = 27
Discount% = (27/135) * 100 = 20%
Question 36
A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?
A
Rs 8.81
B
Rs 9.81
C
Rs 11.81
D
Rs 7.2
Question 36 Explanation: 
85 : 9 = 105 : x
x = (9 × 105 / 85)
x = Rs 11.81
Question 37
If the manufacturer gains 10 %, the wholesale dealer 15 % and the retailer 25 %, then find the cost of production of a table if the retail price was Rs 1265?
A
Rs. 750
B
Rs. 800
C
Rs. 850
D
Rs. 900
Question 37 Explanation: 
Let the cost of Production = Rs. P
Then, as per question,
=>(125100∗115100∗110100∗P)=1265
=>253160P=1265
=>P=800
Question 38
A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is?
A
12%
B
13%
C
14%
D
15%
Question 38 Explanation: 
Suppose he bought 5 kg and 3 kg of tea
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150
Selling price = Rs. (8 x 21) = Rs. 168
Profit = 168 - 150 = 18
So, Profit % = (18/150) * 100 = 12%
Question 39
A shopkeeper sold an article for Rs 2564.36. Approximately what was his profit percent if the cost price of the article was Rs 2400?
A
4%
B
5%
C
6%
D
7%
Question 39 Explanation: 
Gain % = (164.36 * 100 / 2400) = 6.84 % = 7% approx
Question 40
A shopkeeper cheats to the extent of 10% while buying and selling, by using false weights. His total gain is?
A
20%
B
21%
C
22%
D
23%
Question 40 Explanation: 
Gain% = [(100 + common gain%)2 / 100) − 100]%
=[(100 + 10)2 / 100) − 100]%
= [(12100 – 10000) /100]%
= 21%Gain
Question 41
The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs 3. The ratio of two selling prices is?
A
51:52
B
52:53
C
53:54
D
54:55
Question 41 Explanation: 
Let the Cost price of article is Rs. x
Required ratio = (104% of x) / (106% of x)
= 104 / 106
= 52 / 53
= 52:53
Question 42
A man gains 20% by selling an article for a certain price. If he sells it at double the price, the percentage of profit will be?
A
130%
B
140%
C
150%
D
160%
Question 42 Explanation: 
Let the C.P. = x, Then S.P. = (120 / 100)x = 6x / 5 New S.P. = 2 (6x / 5) = 12x / 5 Profit = 12x / 5 - x = 7x / 5 Profit% = (Profit / C.P.) * 100 => (7x / 5) * (1 / x) * 100 => 140 %
Question 43
If the cost price of 12 pens is equal to the selling price of 8 pens, the gain percent is?
A
12%
B
30%
C
50%
D
60%
Question 43 Explanation: 
Let the cost price of 1 pen is Re 1
Cost of 8 pens = Rs 8
Selling price of 8 pens = 12
Gain = 12 - 8 = 4
Gain%=(GainCost ∗ 100)% = (48 ∗ 100)% = 50%
Question 44
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25% then determine the value of x?    
A
14
B
15
C
16
D
17
Question 44 Explanation: 
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x
S.P. of x articles = Rs. 20
Profit = Rs. (20 - x)
Therefore, [(20 - x / x) * 100 = 25]
=> 2000 - 100x = 25x
=> 125x = 2000
=> x = 16
Question 45

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A
70%
B
80%
C
90%
D
None of these
Question 45 Explanation: 
Let C.P.= Rs. 100
Then, Profit = Rs. 320,
S.P. = Rs. 420
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295 / 420) * 100 = 70%(approx)
Question 46

If the cost price of 12 items is equal to the selling price of 16 items, the loss percent is?

A
20%
B
25%
C
30%
D
35%
Question 46 Explanation: 
Let the Cost Price of 1 item = Re. 1
Cost Price of 16 items = 16
Selling Price of 16 items = 12
Loss = 16 - 12 = Rs 4
Loss % = (4 / 16) * 100 = 25%
Question 47

A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 1 less, he would have made a profit of 10%. The C.P. of the article was?

A
Rs 100
B
Rs 150
C
Rs 200
D
Rs 250
Question 47 Explanation: 
Let original Cost price is x
Its Selling price = 105 / 100 * x = 21x / 20
New Cost price = 95 / 100 * x = 19x / 20
New Selling price = 110 / 100 * 19x / 20 = 209x / 200
[(21x / 20) - (209x / 200)] = 1
x = 200
Question 48

A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of that item?

A
Rs. 660
B
Rs. 760
C
Rs. 860
D
Rs. 960
Question 48 Explanation: 
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P
= 80% of 1200
= 80/100 * 1200
= 960
Question 49
Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it?
A
Rs. 22000
B
Rs. 24000
C
Rs. 26000
D
Rs. 28000
Question 49 Explanation: 
calculate all Cost price, then get 150% of CP
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Question 50
A plot is sold for Rs. 18,700 with a loss of 15%. At what price it should be sold to get profit of 15%?
A
Rs 25300
B
Rs 22300
C
Rs 24300
D
Rs 21300
Question 50 Explanation: 
Let at Rs x it can earn 15% profit
85 : 18700 = 115 : x , [as loss = 100 -15, Profit = 100 +15]
x = (18700 * 115) / 85
x = Rs. 25300
Question 51
On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is?
A
45
B
50
C
55
D
60
Question 51 Explanation: 
(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720
C.P. of 1 ball = Rs 720 / 12= Rs. 60
Question 52
When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
A
21,000
B
24,000
C
25,300
D
25,800
Question 52 Explanation: 
85 : 18700 = 115 : x
x = 18700 x 115 / 85 = 25300
Hence, S.P. = Rs. 25,300
Question 53
Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent ?
A
30
B
40
C
50
D
44
Question 53 Explanation: 
C.P. of 30 articles = Rs. (5 / 6) x 30 = Rs. 25
S.P. of 30 articles = Rs. (6 / 5) x 30 = Rs. 36
Gain % = (11 /25) x 100% = 44%.
Question 54
Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
A
3.5
B
4.5
C
5.6
D
6.5
Question 54 Explanation: 
Cost Price of 1 toy = Rs. (375/12) = Rs. 31.25
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % = (1.75 / 31.25 * 100)%
= 28 / 5% = 5.6%
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