Profit and Loss Problems  Solutions  Aptitude, Arithmetic Ability Solved Examples
Profit And Loss Problems
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Basic Definitions
Cost price (C.P.): This is the
price at which an article is purchased.
Selling price (S.P.): This is
the price at which an article is sold.
Profit or Gain: If the selling
price is more than the cost price, the difference between them is the profit
incurred.
Loss: If the selling price is
less than the cost price, the difference between them is the loss incurred.
Profit or Loss is always
calculated on the cost price.
Marked price: This is the price
marked as the selling price on an article, also known as the listed price.
Discount or Rebate: This is the
reduction in price offered on the marked or listed price.
Important Formulas to
Remember:
Formula No. 1

15% Profit on an item means,
Cost price = 100%
Selling price = 115%
Profit = 15%

Formula No. 2

15% Loss on an item means,
Cost price = 100%
Selling price = 85%
Loss = 15%

Formula No. 3

Profit and Loss is always calculated on Cost Price or CP

Formula No. 4

Gain Percentage: (Gain %)
Gain % = (Gain x 100)/ C.P.

Formula No. 5

Loss Percentage: (Loss %)
Loss % = (Loss x 100)/ C.P.

Formula No. 6

Selling Price: (S.P)
SP = (100 + Gain %) /100 x C.P

Formula No. 7

Selling Price: (S.P)
SP = (100 – Loss %) /100 x C.P.

Formula No. 8

Cost Price: (C.P.)
C.P. = 100/ (100 + Gain %) x S.P.

Formula No. 9

Cost Price: (C.P.)
C.P. = 100/ (100 – Loss %) x S.P.

Profit and Loss
problems Question and Answers
Ques 1: If the cost price of 12 pens is equal to the selling price
of 8 pens, the gain percent is ?
1)
12%
2)
30%
3)
50%
4)
60%
Answer: Option 3
Explanation:
Friends, we know we will need gain amount to get gain
percent, right. So lets get gain first.
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
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%Gain%=(GainCost∗100)%=(48∗100)%=50%
Ques 2: The cost price of 20 articles is the same as the selling
price of x articles. If the profit is 25%, find out the value of x
1)
13
2)
14
3)
15
4)
16
Answer: Option 4
Explanation:
Let the Cost Price of one article = Rs. 1
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
CP of x articles = Rs. x
CP of 20 articles = 20
Selling price of x articles = 20
Profit = 25% [Given]
⇒(SP−CPCP)=25100=14⇒(20−x)x=14⇒80−4x=x⇒5x=80⇒x=805=16⇒(SP−CPCP)=25100=14⇒(20−x)x=14⇒80−4x=x⇒5x=80⇒x=805=16
Ques 3: 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
1)
Rs. 750
2)
Rs. 800
3)
Rs. 850
4)
Rs. 900
Answer: Option 2
Explanation:
Let the cost of Production = Rs. P
Then, as per question,
Then, as per question,
=>(125100∗115100∗110100∗P)=1265=>253160P=1265=>P=800=>(125100∗115100∗110100∗P)=1265=>253160P=1265=>P=800
Ques 4: 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.
1)
Rs. 22000
2)
Rs. 24000
3)
Rs. 26000
4)
Rs. 28000
Answer: Option 2
Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Ques 5: 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.
1)
130%
2)
140%
3)
150%
4)
160%
Answer: Option 2
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 %
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 %
Ques 6: 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%.
1)
Rs 25300
2)
Rs 22300
3)
Rs 24300
4)
Rs 21300
Answer: Option 1
Explanation:
This type of question can be easily and quickly solved as
following:
Let at Rs x it can earn 15% pr0fit
85:18700 = 115:x [as, loss = 100 15, Profit = 100 +15]
x = (18700*115)/85
= Rs.25300
Let at Rs x it can earn 15% pr0fit
85:18700 = 115:x [as, loss = 100 15, Profit = 100 +15]
x = (18700*115)/85
= Rs.25300
Ques 7: 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
1)
Rs. 660
2)
Rs. 760
3)
Rs. 860
4)
Rs. 960
Answer: Option 4
Explanation:
Here always remember, whenever x% loss,
it means S.P. = (100  x)% of C.P
whenever x% profit,
it means S.P. = (100 + x)% of C.P
it means S.P. = (100  x)% of C.P
whenever 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
= 80% of 1200
= 80/100 * 1200
= 960
Take
a Test Now

Ques 8. If the
cost price is 25% of selling price. Then what is the profit percent.
1)
150%
2)
200%
3)
300%
4)
350%
Answer: Option 3
Explanation:
Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = 75/25 * 100 = 3005
then C.P. = 25
Profit = 75
Profit% = 75/25 * 100 = 3005
Ques 9: A
bathing soap marked at Rs.80 is sold for Rs.68.Find the rate of discount.
Solution: Marked price = (M.P) = Rs.80
Selling price = (S.P) = Rs.68
Discount amount = Rs. 80 – 68 = Rs.12
Therefore, Rate of discount = Discount x 100 / M.P
= 12 x 100 / 80 = 120 / 8 = 15%
Hence the answer is 15%
Ques 10: Rahul bought a computer for Rs.52,000 and spent
Rs.4000 on its repairs. If he sells at Rs.47,000 then what will be his loss
percentage?
Solution: Rahul bought the computer at
Rs.52, 000
Amount for repairing = Rs.4000
Total Cost price of the computer = Rs.52, 000 + Rs.4000 =
Rs.56,000
Selling price = Rs.47,000
Therefore the amount of loss = CP _ SP = 56,000 – 47,000 =
Rs.9000
Loss % = loss x 100 /CP = 9000 x 100 / 56,000 = 900/56
225/14 % = 16 1/14 %
Ques 11: A seller gains the cost of 40 dozen apples by selling
25 dozen of apples. Then the gain percent is:
Solution: Given that the
cost price (CP) of 40 dozen of apples is equal to selling of 25 dozen of
apples.
Let the CP of 1 dozen of apple = Rs.1
Therefore CP of 40 dozen apples = Rs.40
Given, SP of 25 dozen apples = Rs.40
Then SP of 1 dozen apples = Rs.40/25 = Rs.8/5
Therefore profit of 1 dozen apples = Rs.(8/5 – 1) (SP – CP)
= Rs.3/5
Then profit % = 3/5 x 100 = 60%
Ques 12: Madhesh bought 100 dozen of pins at Rs.10 per dozen.
He spent Rs.500 on a particular tax and he sold them at Rs. 1 per each pin.
What was his profit or loss percent?
Solution: Cost price of 1 dozen of pins =
Rs.10
Cost price of 100 dozen of pins = Rs. 100 x 10 = Rs.1000
Aamount of tax paid = Rs.500
Therefore total cost price = 1000 + 500 = Rs.1, 500
Selling price of total number of pins = 100 x 12 x 1 = Rs.
1,200
Therefore, loss = C.P – S.P = 1500 – 1200 = Rs.300
And loss % = loss x 100 / c.p = 100 x 100 / 1500 = 100/15 %
= 20/3 % = 6 2/3 %
Ques 13: Samy sold his dining table set at a loss of 20%. If
he had sold it for Rs 800 more, he would have received a profit of 5%. Find the
cost price.
Solution: Let the cost price be Rs 100
So when C.P = 100, loss of 20% means
S.P = 100 – 20 = 80
Profit of 5% means S.P = 100 + 5 = 105
The difference of two S.P = 105 – 80 = 25
If the difference is 25, C.P = Rs 100
If the difference is Rs 800, C.P = (100 / 25) x 800
C.P = Rs 3200
Ques 13: 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
1)
4%
2)
5%
3)
6%
4)
7%
Answer:
Option 4
Explanation:
Gain % = (164.36*100/2400) = 6.84 % = 7% approx
Ques 14: A TV is purchased at Rs. 5000 and sold at Rs. 4000, find
the lost percent.
1)
10%
2)
20%
3)
25%
4)
28%
Answer: Option 2
Explanation:
We know, C.P. = 5000
S.P. = 4000
Loss = 5000  4000 = 1000
Loss%=(LossCost∗100)%=(10005000∗100)%=20%
Loss%=(LossCost∗100)%=(10005000∗100)%=20%
Ques 15: 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
1)
70%
2)
80%
3)
90%
4)
None of above
Answer: Option 1
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)
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Ques 16: 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
1)
Rs 100
2)
Rs 150
3)
Rs 200
4)
Rs 250
Answer: Option 3
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
Ques 17: 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%
1)
Rs 8.81
2)
Rs 9.81
3)
Rs 10.81
4)
Rs 11.81
Answer: Option 4
Explanation:
85: 9 = 105: x
x= (9×105/85)
= Rs 11.81
Ques 18: Akhil purchased 70kg vegetable at Rs. 420, then sold them
at the rate of Rs. 6.50 per kg, find the profit percent.
1)
813%
2)
713%
3)
613%
4)
513%
Answer: Option 1
Explanation:
Please note in this type of
questions, get the value of 1 kg to solve this question, lets solve it.
C.P. of 1 Kg = 420/70 = Rs. 6
Selling Price = 6.50
Gain = Rs. 0.50
Gain%=.506∗100=813%
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Ques19: A man bought some toys at the rate of 10 for Rs. 40
and sold them at 8 for Rs. 35. Find his gain or loss percent.
Solution: Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%
Ques 20: The cost price of 10 pens is the same as the selling
price of n pens. If there is a loss of 40%, approximately what is the value of
n?
Solution: Let the price of each pen be
Re. 1.
Then the cost price of n pens is Rs. n and the selling price
of n pens is Rs. 10.
Loss = n10.
Loss of 40% →
(loss/CP)*100 = 40
Therefore, [(n10)/n]*100 = 40 → n = 17 (approx)
Profit and Loss Arithmetic
Ability Solved Examples
Ques 1: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of
rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg.
His profit percent is:
1)
No profit, no loss
2)
5%
3)
8%
4)
10%
Answer: 2
Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 +
1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain: (80/1600 *100) % =5%
Ques 2: By selling 45 lemons for Rs 40, a man loses 20 %. How many
should he sell for Rs 24 to gain 20 % in the transaction?
1)
16
2)
18
3)
20
4)
22
Answer: 2
Explanation:
Let S.P. of 45 lemons be Rs. x.
Then, 80: 40 = 120: x or
x = = 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold = 18.
Ques 3: If books bought at prices ranging from Rs. 200 to Rs. 350
are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest
possible profit that might be made in selling eight books?
1)
600
2)
1200
3)
1800
4)
none of these
Answer: 3
Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8) = Rs. 3400.
Required profit = Rs. (3400  1600) = Rs. 1800.
Ques 4: A man buys oranges at Rs 5 a dozen and an equal number at
Rs 4 a dozen. He sells them at Rs 5.50 a dozen and makes a profit of Rs 50. How
many oranges does he buy?
1)
30 dozens
2)
40 dozens
3)
50 dozens
4)
60 dozens
Answer: 3
Explanation:
Cost Price of 2 dozen oranges Rs. (5 + 4) = Rs. 9.
Sell price of 2 dozen oranges = Rs. 11.
If profit is Rs 2, oranges bought = 2 dozen.
If profit is Rs. 50, oranges bought = (2/2) * 50 dozens = 50
dozens.
Ques 5: 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
1)
Rs 100
2)
Rs 150
3)
Rs 200
4)
Rs 250
Answer: 3
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
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Questions and Answers
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