Percentage and Profit
Percentage and Profit
Percentage and Profit
PERCENTAGE - PROFIT
AND LOSS
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100
100
14400
votes
polled
=
= 900 100 = 90000
16
Total number of eligible voters = 100000
(Given)
Number of voter who did not vote = eligible voters votes polled
= 100000 90000 = 10000
Thus, percentage of the number of voters who did not vote
10000
10000
100
% = 10%
=
% =
1000
100000
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60
8000 = 60 80 =4800
100
Number of girls candidates = 8000 4800 = 3200
Number of passed boys = 80% of number of boys
80
4800 = 80 48 = 3840
100
Number of passed girls = 90% of number of girls
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90
3200 = 90 32 = 2880
=
100
Thus number of passed candidates = 3840 + 2880 = 6720
and number of failed candidates = 8000 6720 = 1280
Hence, 1280 candidates are failed.
6. Out of 120 employees in a company, 80% are males. Eighty male
employees and three-fourth of the female employees are married. In
aggregate, what percent of companys employees are married?
Ans. Total number of employees in the company = 120
Number of males employees in the company = 80% of 120
80
120 = 96
100
Number of female employees in the company = 120 96 = 24
Number of married employees in the company
= 80 + of 24 = 80 + 18 = 98
4
Question Bank
2
Hence, 81 % of companys employees are married.
3
7.(i) A number 3.625 is wrongly read as 3.265; find the percentage error.
(ii) A number 5.78 103 is wrongly written as 5.87 103 ; find the
percentage error.
Ans. (i) Correct number = 3.625
Number wrongly read = 3.265
Then error = (3.625 3.265) = 0.360
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0.360
100%
3.625
360
36000
100% =
% = 9.93%
=
3625
3625
Hence, percentage error is 9.93%.
(ii) Correct number = 5.78 103
Number wrongly written as = 5.87 103
Thus, error = 5.87 103 5.78 103 = 0.09 103
0.09 103
0.09
100%
100%
=
5.78
5.78 103
9
900
=
100% =
% = 1.56%
578
578
Hence, percentage error is 1.56%.
8. Bhola Ram gave 35% of his money to his elder son and 40% of the
remainder to the younger son. Now, he is left with Rs 11700. How
much money had he?
Ans. Let Bhola Ram had Rs x.
35 x
100
35 x 65 x
Remaining amount = Rs
=
100
100
Math Class VIII
Question Bank
65 x 40
26
=
x
100 100 100
65 x 26 39
x =
x
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5
5x
=
100 100
5 x 95 x
=
100 100
95 x 8
76
=
x
Those people who left the town =
100 100 1000
95 x
76
x
Hence, remaining population of the town =
100 1000
950 x 76 x 874
=
x
=
1000
1000
43700 1000
874
x
=
= 50000
x = 43700
874
1000
Hence, population of the town at the beginning was 50000.
10. A and B are two towers. The height of tower A is 20% less than that
of B. How much per cent is Bs height more than that of A?
Ans. Let height of tower B = 100 m
Since, height of tower A is 20% less than B
Question Bank
20
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100
310 = 500
62
Hence, 500 candidates appeared in the examination..
12. In a combined test in History and Civics; 36% candidates failed in
History; 28% failed in Civics and 12% in both; find :
(i) the percentage of passed condidates
(ii) the total number of candidates appeared, if 208 candidates have
failed.
Ans. Candidates failed only in History = 36% 12% = 24%
Candidates failed only in Civics = 28% 12% = 16%
Candidates failed in both subjects = 12%
Total failed candidates = 24% + 16% + 12% = 52%
(i) Thus percentage of passed candidates = 100% 52% = 48%
Question Bank
100
52
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20
1
x
x = x=
100
5
5
5
x
x=
Number of died parrots = 5% of x =
100
20
x x
4x + x
x
+
x
5 20
20
5x
x 4 x x 3x
= x =
=
= x
20
4
4
4
3x
45 3x
3 x 27 x 60 x 27 x 33x
=
=
4
80
80
80
As per condition,
Math Class VIII
Question Bank
33x
33x = 33 80
= 33
80
33 80
x=
x = 80
33
Hence, Nandani purchased 80 parrots.
14. A lunch interval of half an hour is 5% of total office hours. Calculate
(i) the total office hours
(ii) the working hours
1
Ans. (i) 5% of total office hours = hour
2
5
1
of total office hours = hour
100
2
100
hours = 10 hours.
total office hours =
5 2
1
(ii) Working hours = 10 hours hours
2
1
19
1
10
hours = 9 hours.
=
hours =
2
2
2
15. Price of bananas has changed from 5 for a rupee to 4 for a rupee.
Find the percentage increase in the price.
Ans. Original price of 5 bananas = Rs 1
1
Original
price
of
1
banana
=
Rs
5
Changed price of 4 bananas = Rs 1
1
Changed
price
of
1
banana
=
Rs
4
1
1 1
54
Increased price = Rs = Rs
=
Rs
20
4 5
20
1
20
Hence, percentage increased price = 1 100%
5
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1 5
100%
20 1
1
= 100% = 25%
4
16. Two numbers are respectively 25% and 35% less than a third number.
What percent is the second number of the first?
Ans. Let the third number be x
Z
B
25
75
3
x= x
Then, first number = 1
x =
100
4
100
35
65
13
x
=
x
x
And, second number = 1
=
100
20
100
13
x
13
4
20
x 100%
100% =
Thus, required percentage =
3
20
3x
x
4
13
13
260
100% = 20% =
%
=
53
3
3
2
= 86 %
3
17. 75% of the students in a class VIII passed an exam. If 2 more students
had passed the exam, 80% would have been successful. How many
students were there in the class VIII?
Ans. Let the total number of students in the class VIII be x,
Number of passed students in the calss VIII = 75% of x
75
75 x
x=
=
100
100
As per condition,
75 x
+ 2 = 80% of x
100
75 x
80 x
75 x
80
+2=
+2=
x
100
100
100
100
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80 x 75 x
5x
2=
100 100
100
x
x
=2
2=
20
20
x = 2 20
x = 40
Hence, the total number of students in class VIII were 40.
18. The monthly salary of a school teacher in 2005 was Rs. 12000. It
increased by 10% in 2006 and again by 10% in 2007. What is his
salary in 2007?
Ans. Monthly salary of the school teacher in 2005 = Rs 12000
2=
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10
11
110
12000
= Rs
=
Rs
1200
10
100
= Rs 11 1200 = Rs 13200
Monthly salary of the school teacher in 2007
10
1
+
=
Rs 13200
100
11
110
13200
13200
=
Rs
= Rs
10
100
= Rs 11 1320 = Rs 14520
Hence, monthly salary of the school teacher in 2007 = Rs 14520
19. Dollys height increased by 20% last year and by 15% this year. What
is the total percent increase in 2 years?
Ans. Let the original height of Dolly be x
20
120
120 x
x
=
=
Increased height in last year = 1 +
100
100
100
15 120 x
100 100
Math Class VIII
10
Question Bank
=
100 100 20 5
100
138 x
138 x 100 x 38 x
x =
=
Total increases in 2 years =
100
100
100
38 x
Total percentage increases in 2 years = 100 100%
x
38 x
100% = 38%
=
100 x
Hence, 38% increase in 2 years.
20. Price of a commodity decreased by 10% last year and increased by
20% this year. Find the percentage change in two years.
Ans. Let the price of commodity be Rs x
When the price of commodity is decreased by 10% in last year
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10
90
9x
x = Rs
= Rs
10
10
When the price of commodity increased by 20% in this year
9x
20
11
Question Bank
2x
= 25 100% = 2 x 100%
x
25 x
= 2 4% = 8%
21. The length and the breadth of a rectangle are 10 cm and 8 cm. If its
length increases by 15% and breadth by 20%, find the percentage
increase in its area.
Ans. Length of rectangle increases by 15% and the breadth increases by
20% (given)
15
115
115
10cm =
cm = 11.5 cm
=
100
10
20
30.4
100 % =
5 %
Percentage increase in area =
80
100
100
100
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12
Question Bank
50
100 x + 50 x 150 x
x=
=
100
100
100
150 x
150 x 100
100
100 %
Thus, required percent =
100% =
120 x
100 120 x
100
150 100
1500
=
% = 125%
%=
120
12
23. Two numbers are respectively 30 percent and 40 percent less than a
third number. What percent is the second of the first?
Ans. Let the third number be x
Second number = x +
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30 x 100 x 30 x 70 x 7 x
=
=
=
100
100
100 10
40 x 100 x 40 x 60 x 6 x
=
=
and second number = x
=
100
100
100 10
6x
Thus, required percentage = 10 100
7x
10
6 x 10
600
5
100 =
= 85 %
=
10 7 x
7
7
5
Hence, 85 percentage of the first is the second.
7
24. During 2006, the production of a publication factory decreased by
25%. But, during 2007, it (production) increased by 40% of what it
was at the beginning of 2007. Calculate the resulting change (increase
or decrease) in production during these two years.
Ans. Let at the begining of 2006, production = 100
decrease in production = 25%
Thus, new production = 100 25 = 75
In 2007, it is increased by 40%
First number = x
13
Question Bank
75 40
= 30
100
New production = 75 + 30 = 105
Resulting change in two years (increase) = 105 100 = 5
Hence, precentage change in increase in production
5
100% = 5%
=
100
25. Motilal bought a certain number of oranges at Rs 60 per score and
sold them at 20% profit. Find the selling price of each orange.
Ans. Cost price of 20 oranges = Rs 60
( 1 score = 20)
60
= Rs 3
Cost price of 1 orange =
20
Profit = 20%
3 120 360
=
= Rs 3.60
Selling price of 1 orange =
100
100
26. Nakvi sells two articles for Rs 4,500 each, making 25% profit on
one and 25% loss on the other. Find:
(i) CP of each article.
(ii) total CP of both the articles.
(iii) total SP of both the articles.
(iv) profit % or loss % on the whole.
Ans. (i) Selling price of two articles = Rs 4500 each.
Increase in production =
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Question Bank
= 56
= 56
25
25
25
25
56 25
, x = 350.
x=
4
Hence, cost price of the wine bottle = Rs 350.
28. The selling price of 18 mangoes is equal to the cost price of 21
mangoes. Find the gain or loss per cent.
Ans. Let cost price of each mangoes = Re 1
Cost price of 18 mangoes = Rs 18
Selling price of 18 mangoes = Cost price of 21 mangoes = Rs 21
Gain = Rs (21 18) = Rs 3
3
50
2
100% = % = 16 %
Hence,
gain
%
=
Math Class VIII
153
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18
3
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29. The cost price of 12 fans is equal to the selling price of 16 fans. Find
the gain or loss per cent.
Ans. Let selling price of one fan = Rs 100
Selling price of 16 fans = Rs 100 16 = Rs 1600
and cost price of 12 fans = Rs 1600
1600
400
= Rs
Cost price of one fan =
12
3
Loss = cost price selling price
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100
400 100 400 300
=
= Rs
=
Rs
3
1
3
3
100
100
Loss 100
3
%=
%
Loss percent =
400
cost price
3
100 100 3
% = 25%
=
3 400
30. A man buys two bats, one for Rs. 340 and the other for Rs 260. He
sells the first bat at a gain of 15% and the second one at a loss of
15%. Find the gain or loss per cent in the whole transaction.
Ans. Cost price of first bat = Rs 340
15
340 = Rs 51
100
Selling price of first bat = Rs (340 + 51) = Rs 391
Now, cost price of second bat = Rs 260
15
Loss = 15% of Rs 260 = Rs
260 = Rs 39
100
Selling price of second bat = Rs (260 39) = Rs 221
Total selling price of two bats = Rs (391 + 221) = Rs 612
Gain = Rs (612 600) = Rs 12
12
100% = 2%
Hence, gain% =
600
Hence, his gain in whole transaction is 2%.
16
Question Bank
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20
576 = Rs 115.20
100
Thus, selling price of 12 dozen note-books
= Rs (576 + 115.20) = Rs 691.20
Selling price of 20 dozen note-books
= Rs (422.40 + 691.20) = Rs 1113.60
Whole gain = Rs (1113.60 960) = Rs 153.60
153.60
100% = 16%
960
Hence, his gain percent in whole transaction is 16%.
32. A shopkeeper buys a certain number of pens. If the selling price of 5
pens is equal to the cost price of 7 pens, find his profit or loss
percentage.
Ans. Let the cost price of 7 pens be Rs x.
Gain% =
x
7
As per condition,
Selling price of 5 Pens = Rs x
Selling price of 1 Pen = Rs
Math Class VIII
17
x
5
Question Bank
x
x
Rs
5
7
2x
7 x 5x
= Rs
=
Rs
35
35
2x
Profit
100% = 35 100%
Profit % =
x
cost price
7
2x 7
2
100% = 100% = 2 20% = 40%
=
35 x
5
Hence, profit percentage is 40%.
33. Coffee costing Rs 100 per kg was mixed with chicory costing Rs. 50
per kg in the ratio 5 : 2 for a certain blend. If the mixture was sold at
Rs. 90 per kg. Find the gain or loss per cent.
Ans. Cost price of 1 kg of coffee = Rs 100
Cost price of 5 kg of coffee = Rs 5 100 = Rs 500
Cost price of 1 kg of chicory = Rs 50
Cost price of 2 kg of chicory = Rs 2 50 = Rs 100
Cost price of (5 + 2) kg of mixture
= Rs (500 + 100) = Rs 600
Now, selling price of 1 kg of mixture = Rs 90
Selling price of 7 kg of mixture = Rs 7 90 = Rs 630
Gain = Rs (630 600) = Rs 30
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30
100% = 5%
600
34. A sells a bicycle to B at a profit of 20% and B sells it to C at a profit
of 5%. If C pays Rs 1890, what did A pay for it?
Ans. Cs cost price for the cycle = Rs 1890
or Bs selling price = Rs 1890
gain = 5%
18
Question Bank
Bs cost price =
1890 100
= Rs 1800
105
or As selling price = Rs 1800
As gain = 20%
= Rs
Z
B
1800 100
1800 100
= Rs
= Rs 1500
100 + 20
120
Hence, A will pay Rs 1500 for bicycle.
35. Roma sold a watch to Monu at 12% gain and Monu had to sell it to
Lavish at a loss 5%. If Lavish paid Rs 1330, how much did Roma
pay for it?
Ans. Let cost price of the watch by Roma be Rs x
12
3x
x=
Profit = 12% of x =
100
25
3 x 25 x + 3x 28 x
=
Selling price of the watch by Roma = x +
=
25
25
25
28 x
Cost price of the watch by Monu =
25
28 x
5 28 x 7 x
=
=
Loss = 5% of
25 100 25 125
28 x 7 x
As cost price = Rs
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Question Bank
36. Dhani Ram purchased a cow for Rs 6000 and a buffalo for
Rs 12000. He sold the buffalo at a profit of 15% and the cow at a
loss of 10%. Calculate his overall profit or loss percentage.
Ans. Cost price of cow = Rs 6000
and cost price of buffalo = Rs 12000
Thus, total cost price of cow and buffalo = Rs (6000 + 12000)
= Rs 18000
Dhani Ram sold the cow at the loss of 10%, then selling price of cow
Z
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10
= 1
of (cost price of cow)
100
90
10
6000
6000
=
Rs
= Rs 1
100
100
= Rs 90 60 = Rs 5400
Dhani Ram sold the buffalo at the profit of 15%
15
15
= Rs 1 +
12000
100
115
12000
= Rs
100
= Rs 115 120 = Rs 13800
Selling price of cow and buffalo = Rs (5400 + 13800)
= Rs 19200
Thus, profit = selling price cost price
= Rs (19200 18000) = Rs 1200
Hence,
Profit
100 %
profit% =
Cost price
1200
100 %
=
18000
20
Question Bank
1200
120
20
2
%=
%= %=6 %
180
18
3
3
2
Hence, overall percentage of Dhani Ram is 6 % .
3
37. By selling an almirah for Rs 3920, a shopkeeper would gain 12%. If
it is sold for Rs 4375, find his gain or loss percentage.
Ans. When selling price of almirah = Rs 3920 and gain = 12%
then cost price P = ?
Z
B
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D
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IN
12
100 + 12
Rs
3920
=
of CP
100
3920
100
CP = Rs
112
= Rs 35 100 = Rs 3500
When cost price of almirah = Rs 3500
and selling price of almirah = Rs 4375
Then, gain = SP CP = Rs (4375 3500) = Rs 875
gain
100 %
Hence, gain% =
CP
875
875
100 % =
% = 25%
=
3500
35
21
Question Bank
1
Rs
1334
=
CP
100
1334
100
Cost price of bicycle = Rs
92
1334
25
Cost price of bicycle = Rs
23
Cost price of bicycle CP = Rs 58 25 = Rs 1450
Now, CP = Rs 1450
1
25
= %
Profit on bicycle = 12
2% 2
25
25
100
1
Selling price of bicycle = 1 + 1450
8
9
Selling price of bicycle = 1450
8
Selling price of bicycle = (9 181.25) = Rs 1631.25
39. Sohan bought a certain number of note-books for Rs 600. He sold
1
of them at 5 per cent loss. At what price should he sell the
4
remaining note-books so as to gain 10% on the whole?
Ans.
Cost price of note-books = Rs 600
Gain desired on the whole = 10%
Then total selling price of all the note-books
(100 + gain% ) CP = 100 + 10
=
Rs 600
100
100
110
600 = Rs 660
= Rs
100
Math Class VIII
22
Question Bank
Z
B
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1
1
of the books = Rs 600 = Rs 150
4
4
Loss on these note-books = 5%
Then, selling price of these note-books
(100 Loss % )
(100 5)
CP =
Rs 150
=
100
100
95
14250
150 = Rs
= Rs
= Rs 142.50
100
100
Thus, required selling price of the remaining note-books
= Rs(660 142.50) = Rs 517.50
40. Sanjay sold a bicycle at 5% profit. If the cost had been 30% less and
the selling price Rs 63 less, he would have made a profit of 30%.
What is the cost price of the bicycle?
Ans. Let cost price of the bicycle = Rs 100
When profit = 5% ;
S.P. = Rs (100 + 5) = Rs 105
30
100
9
=
Rs
450.
Math Class VIII
23
Question Bank
Cost price of
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41. Mona sold a pressure cooker at a loss of 8%. Had she bought it at
10% less and sold for Rs 88 more, she would have gained 20%.
Find the cost price of the pressure cooker.
Ans. Let the cost price of pressure cooker = Rs 100
loss on pressure cooker = 8%
Then, selling price of pressure cooker = Rs (100 8) = Rs 92
Again, cost price of pressure cooker = Rs (100 10) = Rs 90
gain = 20%
C.P. (100 + gain%)
Thus, selling price of pressure cooker =
100
90(100 + 20)
= Rs
100
90 120
= Rs
= Rs 108
100
Difference in two selling prices (108 92) = Rs 16
If difference is Rs 16, then cost price = Rs 100
Z
B
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A
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N
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100 88
= Rs 550
16
Hence, cost price of pressure cooker is Rs 550.
42. The manufacturing price of a T.V. set was Rs 5000. The company
sold it to a distributor at 16% profit. The distributor sold it to a
dealer at 10% profit. The dealer sold it to a customer at 20% profit.
Find the price the customer paid.
Ans. The manufacturing price of T.V. set = Rs 5000
Profit = 16%
16
100 + 16
=
of Rs 5000
100
116
116
Rs 5000 = Rs
5000
=
100
100
= Rs 116 50 = Rs 5800
24
Question Bank
1
+
=
of Rs 5800
100
10
110
1
+
5800
=
of Rs 5800 = Rs
100
100
= Rs 110 58 = Rs 6380
Thus, cost price of T.V. set for dealer = Rs 6380
Again profit = 20%
Selling price of T.V. set for dealer
Z
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20
= 1 +
of Rs 6380
100
100 + 20
=
of Rs 6380
100
120
120
6380
of Rs 6380 = Rs
=
100
100
= Rs 12 638 = Rs 7656
Hence, the price the customer paid = Rs 7656.
43. A sells an article to B at a profit of 20% and B sells it to C at a loss of
6%. If C pays Rs 846, find how much did A pay for it.
Ans. Let the amount A pays for the article be x
when A sells to B at a profit of 20%
20
price for A.
2
12
12 x
= 1 + Rs x = Rs x = Rs
10
10
10
12 x
i.e. cost price of the article for B = Rs
10
25
Question Bank
= 1
of
cost
price
for
B
=
of
Rs
1
10
100
100
3
12 x
564 x
47 12 x
= 1 of Rs
= Rs
= Rs
10
500
50 10
50
564
x = Rs 846
But, C pays Rs 846, for an article then,
500
500
250
x = Rs 846
= Rs 846
564
282
= Rs 3 250 = Rs 750
Hence, cost price of an article for A = Rs 750
44. Saurav sold an article at a profit of 12%. Had it been sold for
Rs 16 more, the profit would have been 20%. Find, the selling price
of the article.
Ans. Let the selling price of an article be Rs x,
Then, profit on article = 12%
P
1
+
Selling
price
=
of cost price
100
12
Rs x = 1 +
of cost price
100
112
=
of cost price
100
100 x
100
Cost price = Rs
x=
112
112
To make 20% profit,
20
Selling price = 1 +
of cost price
100
Z
B
L
A
A
N
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26
Question Bank
6
1
= 1 + of cost price = of cost price
5
5
100 x
6
6 100 x
= Rs
= of Rs
112
5
5 112
120
6 20 x
x
= Rs
=
Rs
112
112
As per condition,
120
120
x = x + 16
x x = 16
112
112
8x
120 x 112 x
= 16
= 16
112
112
16 112
= Rs 2 112 = Rs 224
Rs
8
Hence, the selling price of the article is Rs 224.
45. After allowing a discount of 15% a navycut was sold for Rs 578.
Find its marked price.
Ans. Let market price of the navycut be Rs x.
Z
B
L
A
A
N
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D
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15
15 x
3x
x = Rs
= Rs
100
100
20
3x
17 x
20 x 3 x
= Rs
=
Rs
20
20
578 20
17 x
x = 680.
= 578 x =
17
20
Hence, market price of the navycut is Rs 680.
46. A coat was bought for Rs 435 after getting a discount of 13%. Find
the marked price of the coat.
Ans. Let marked price of the coat be Rs x
Discount = 15% of Rs x = Rs
27
Question Bank
Discount = 13% of Rs x
13
13 x
x = Rs
= Rs
100
100
13x
100
87 x
100 x 13x
= Rs
=
Rs
100
100
87 x
435 100
= 435 x =
x = 500
100
87
Hence, marked price of the coat is Rs 500.
47. A shopkeeper buys a Tea set for Rs 1200 and marks it 80% above the
cost price. If he gives 15% discount on it, find:
(i) the marked price
(ii) the selling price
(iii) his profit percentage
Ans. (i) Cost price of a tea set = Rs 1200
Marked price of tea set
= Rs1200 + 80% of (Rs 1200)
80
1200
= Rs 1200 +
100
= Rs [1200 + 80 12]
= Rs [1200 + 960] = Rs 2160
(ii) Marked price = Rs 2160, discount = 15%
Selling price = ?
d
Selling price = 1
of marked price
100
15
Selling price = 1
Rs 2160
100
Z
B
L
A
A
N
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Question Bank
85
2160
100
17
2160
Selling price = Rs
20
Selling price = Rs 17 108 = Rs 1836
(iii) Profit = selling price cost price
= Rs (1836 1200) = Rs 636
Profit
100 %
Profit % =
Cost price
Selling price = Rs
Z
B
L
A
A
N
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636
636
100 % =
% = 53%
=
12
1200
48. The cost price of a Reliance mobile is Rs 1600, which is 20% below
the marked price. If the article is sold at a discount of 16%, find:
(i) the marked price
(ii) the selling price
(iii) profit percentage.
Ans. (i) Cost price of Reliance mobile = Rs 1600
Since the cost price of Reliance mobile is 20% below the marked
price.
Let the marked price of Reliance mobile = Rs x
Then, Cost price = Marked price 20% of Marked price
Rs 1600 = x 20% of x
20
x
Rs 1600 = x
100
80 x
Rs 1600 =
100
100
1600
x
=
Rs
80
= Rs 20 100 = Rs 2000
Hence, the marked price of Reliance mobile = Rs 2000
Math Class VIII
29
Question Bank
16
Selling price = 1
of marked price
100
100 16
=
of Rs 2000
100
84
2000 = Rs 84 20 = 1680
= Rs
100
(iii) Profit = selling price cost price = Rs (1680 1600) = Rs 80
Z
B
L
A
A
N
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Profit
100 %
Profit % =
Cost price
80
80
% = 5%.
100 % =
=
16
1600
49. An umbrella was marked 40% above cost price and a discount of
35% was given on its marked price. Find the gain or loss per cent
made by the shopkeeper.
Ans. Let cost price of the umbrella be Rs x.
Marked price of the umbrella = Rs (x + 40% of x)
40
2x
x = Rs x +
= Rs x +
100
5
7x
5x + 2x
= Rs
= Rs 5
5
7x
Discount on umbrella = 35% of Rs
5
35
7x
49 x
= Rs
= Rs
100
5
100
7 x 49 x
5
100
Hence,
30
Question Bank
91x
140 x 49 x
= Rs
= Rs
100
100
100 x 91x
9x
91x
Loss = Rs x
=
Rs
=
Rs
100
100
100
9x
Hence, Loss% =
100% = 9%
100 x
50. Mr Kabuliwala purchased a washing machine for Rs 7660. After
allowing a discount of 12% on its marked price he sells it at a gain
of 10%. Find the marked price.
Ans. Let marked price of the washing machine be Rs x.
Z
B
L
A
A
N
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12
3x
x = Rs
100
25
Thus, selling price of the washing machine
Discount = 12% of Rs x = Rs
22 x
3x
25 x 3 x
=
Rs
= Rs x = Rs
25
25
25
Cost price of the washing machine = Rs 7660
Gain = 10%
Thus, selling price of the washing machine
100 + 10
110
7660 = Rs
7660 = Rs 8426
100
100
22 x
If selling price Rs
, then marked price = Rs x
25
x 25
If selling price Re 1, then marked price = Rs
22 x
25
If selling price Rs 8426, then marked price = Rs
8426
22
= Rs 9575
51. Find a single discount equivalent to two successive discounts of
40% and 5%.
= Rs
31
Question Bank
100
100(100 20) (100 5) (100 1)
=
100 100 100
100 80 95 99 7524
=
=
= Rs 75.24
100 100 100
100
Thus, total amount of discount = Rs (100 75.24) = Rs 24.76
Hence, single discount = 24.76%.
53. If after giving a discount of 10%, a shopkeeper still makes a profit of
12.5%, find how much above the cost price he had marked the prices.
Ans. Let the cost price of the article be Rs x.
Profit is 12.5%
Z
B
L
A
A
N
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Question Bank
12.5
Selling price of article = 1 +
of Rs x
100
112.5
100 + 12.5
x
of
Rs
x
=
Rs
=
100
100
Shopkeeper allows a discount of 10%
10
Selling price = 1
of marked price
100
112.5 x
90
=
of marked price
100
100
112.5 x
9
=
of marked price
100
10
10 112.5 x
Marked price =
9
100
1 112.5 x 112.5
x
=
=
9
10
90
Thus, the excess value to be marked = marked price cost price
Z
B
L
A
A
N
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D
N
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IN
112.5 x
112.5 x
x
Rs x = Rs
= Rs
90
90
112.5 x 90 x
22.5 x
= Rs
= Rs
90
90
100 %
=
cost price
22.5
x
90
22.5
100 %
100
%
=
=
90
33
Question Bank
225
% = 25%
9
Hence, the shopkeeper marks the article above the cost price by 25%.
54. If a shopkeeper marks his goods at 20% above the cost price and
then gives 20% discount, find his gain or loss percentage.
Ans. Let the cost price of an article be Rs x.
Since the dealer marks his goods 20% above the cost price.
Marked price = Cost price + 20% of Cost price
Z
B
L
A
A
N
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D
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IN
20
of Rs x = Rs
= Rs x +
100
= Rs
20 x
x
+
100
120 x
6x
= Rs
100
5
Selling price = 1
of Marked price
100
6x
80
6x
96 x
20
= 1
of
Rs
=
Rs
=
Rs
5
100
5
100
100
Loss = cost price selling price
= Rs x Rs
96 x
= Rs
100
96 x
100
4x
x
100 x 96 x
= Rs
=
Rs
=
Rs
100
25
100
Loss
100 %
Loss% =
Cost price
25
100
x
100
100 % =
=
% =
% = 4%
x
25
25
34
Question Bank
Selling price = 1 +
of Cost price
100
117
17
x
= 1 +
of
Rs
x
=
Rs
100
100
Since the dealer allows a discount of 10%
Z
B
L
A
A
N
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D
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IN
10
Selling price = 1
of Marked price
100
117 x
90
Rs
=
of Marked price
100
100
117 x
9
Rs
=
of Marked price
100
10
117 10
13
x
Marked
price
=
Rs
=
Rs
100
9
10
Thus, the excess value to be marked
= Marked price Cost price
13x
13 x
3x
x = Rs
= Rs
Rs x = Rs
10
10
10
100 %
=
cost price
3x
10
3x
100
=
100
% =
x
10
35
Question Bank
= 100 % = 30%
10
Hence, the dealer marks the article above the cost price by 30%.
Z
B
L
A
A
N
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D
N
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Question Bank