RS Aggarwal Solutions: Exercise 10A - Profit & Loss | Mathematics (Maths) Class 8 PDF Download

 Page 1


Question:1
Find the gain or loss per cent when:
i
CP = Rs 620 and SP = Rs 713
ii
CP = Rs 675 and SP = Rs 630
iii
CP = Rs 345 and SP = Rs 372.60
iv
CP = Rs 80 and SP = Rs 76.80
Solution:
i CP = Rs. 620 SP = Rs. 713Since SP > CP, there is a gain. Gain = 713 - 620 = Rs. 93Gain percentage =
gain
CP
×100 %                              =
93
620
×100 %                               = 15 %
ii
CP = Rs 675 SP = Rs 630Since SP < CP, there is a loss. Loss = 675 - 630 = Rs. 45Loss percentage =
Loss
CP
×100 %               =
45
675
×100 %                = 6
2
3
%
iii
CP = Rs. 345 SP = Rs. 372. 60Since SP > CP, there is a gain. Gain = 372. 60 - 345 = Rs. 27. 6Gain percentage =
gain
CP
 ×100 %               =
27.6
345
×100 %                =
2760
345
%           
iv
CP = Rs 80 SP = Rs 76. 80Since SP < CP, there is a loss. Loss = 80 - 76. 80 = Rs. 3. 2Loss percentage =
loss
CP
 ×100 %                               =
3.2
80
×100 %                              =
32
80
×
Question:2
Find the selling price when:
i
CP = Rs 1650 and gain% = 4%
ii
CP = Rs 915 and gain% = 6
2
3
%
iii
CP = Rs 875 and loss% = 12%
iv
CP = Rs 645 and loss% = 13
1
3
%
Solution:
i
CP = Rs. 1650Gain percentage = 4 %SP =
(100+gain %)
100
×CP =
(100+4)
100
×1650 =
104×1650
100
= Rs. 1716
ii
CP = Rs. 915Gain percentage = 6
2
3
% =
20
3
%SP =
(100+gain %)
100
×CP =
100+
20
3
100
×915 =
320
3
100
×915 =
320
3
×
1
100
×915 = Rs. 976
iii
CP = Rs. 875Loss percentage = 12 %SP =
(100-loss %)
100
×CP =
(100-12)
100
×875 =
77000
100
= Rs. 770
iv
CP = Rs. 645Loss percentage = 13
1
3
% =
40
3
%SP =
(100-loss %)
100
×CP =
100-
40
3
100
×645 =
300-40
3
100
×645 =
260
3
×
1
100
×645 = Rs. 559
Question:3
Find the cost price when:
i
SP = Rs 1596 and gain% = 12%
ii
SP = Rs 2431 and loss% = 6
1
2
%
iii
SP = Rs 657.60 and loss% = 4%
iv
SP = Rs 34.40 and gain% = 7
1
2
%
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Page 2


Question:1
Find the gain or loss per cent when:
i
CP = Rs 620 and SP = Rs 713
ii
CP = Rs 675 and SP = Rs 630
iii
CP = Rs 345 and SP = Rs 372.60
iv
CP = Rs 80 and SP = Rs 76.80
Solution:
i CP = Rs. 620 SP = Rs. 713Since SP > CP, there is a gain. Gain = 713 - 620 = Rs. 93Gain percentage =
gain
CP
×100 %                              =
93
620
×100 %                               = 15 %
ii
CP = Rs 675 SP = Rs 630Since SP < CP, there is a loss. Loss = 675 - 630 = Rs. 45Loss percentage =
Loss
CP
×100 %               =
45
675
×100 %                = 6
2
3
%
iii
CP = Rs. 345 SP = Rs. 372. 60Since SP > CP, there is a gain. Gain = 372. 60 - 345 = Rs. 27. 6Gain percentage =
gain
CP
 ×100 %               =
27.6
345
×100 %                =
2760
345
%           
iv
CP = Rs 80 SP = Rs 76. 80Since SP < CP, there is a loss. Loss = 80 - 76. 80 = Rs. 3. 2Loss percentage =
loss
CP
 ×100 %                               =
3.2
80
×100 %                              =
32
80
×
Question:2
Find the selling price when:
i
CP = Rs 1650 and gain% = 4%
ii
CP = Rs 915 and gain% = 6
2
3
%
iii
CP = Rs 875 and loss% = 12%
iv
CP = Rs 645 and loss% = 13
1
3
%
Solution:
i
CP = Rs. 1650Gain percentage = 4 %SP =
(100+gain %)
100
×CP =
(100+4)
100
×1650 =
104×1650
100
= Rs. 1716
ii
CP = Rs. 915Gain percentage = 6
2
3
% =
20
3
%SP =
(100+gain %)
100
×CP =
100+
20
3
100
×915 =
320
3
100
×915 =
320
3
×
1
100
×915 = Rs. 976
iii
CP = Rs. 875Loss percentage = 12 %SP =
(100-loss %)
100
×CP =
(100-12)
100
×875 =
77000
100
= Rs. 770
iv
CP = Rs. 645Loss percentage = 13
1
3
% =
40
3
%SP =
(100-loss %)
100
×CP =
100-
40
3
100
×645 =
300-40
3
100
×645 =
260
3
×
1
100
×645 = Rs. 559
Question:3
Find the cost price when:
i
SP = Rs 1596 and gain% = 12%
ii
SP = Rs 2431 and loss% = 6
1
2
%
iii
SP = Rs 657.60 and loss% = 4%
iv
SP = Rs 34.40 and gain% = 7
1
2
%
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Solution:
i SP = Rs. 1596Gain percentage = 12 %CP =
100
(100+gain %)
×SP =
100
(100+12)
×1596 = Rs. 1425
ii
SP = Rs. 2431 Loss percentage = 6
1
2
% =
13
2
%CP =
100
(100-loss %)
×SP =
100
100-
13
2
×2431 =
100×2
187
×2431 = Rs. 2600
iii
SP = Rs. 657. 60 Loss percentage = 4 %CP =
100
(100-loss %)
×SP =
100
(100-4)
×657. 60 = Rs. 685
iv
SP = Rs. 34. 40 Gain percentage = 7
1
2
% =
15
2
%CP =
100
(100+gain %)
×SP =
100
100+
15
2
×34. 40 =
100×2
215
×34. 40 = Rs. 32
Question:4
Manjit bought an iron safe for  12160 and paid  340 for its transportation. Then, he sold it for  12875. Find his gain per cent
Solution:
CP of the iron safe = 12,160
Money spent on transportation = 340
Total CP = 12,160 + 340 = 12,500
SP of the iron safe = 12,875
Profit = SP - CP = 12,875 - 12,500 = 375
? Profit% = 
Profit
CP
×100 %
=
375
12500
×100 % = 3 %
 
Question:5
Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or
loss?
Solution:
CP of the car = Rs. 73500Repairs = Rs. 10300Insurance = Rs. 2600Total CP = 73500 +10300 +2600 = Rs. 86400SP = Rs. 84240Since SP < CP, Robin has a loss. Loss = 86400 -84240
Question:6
Hari bought 20 kg of rice at  36 per kg and 25 kg of rice at  32 per kg. He mixed the two varieties and sold the mixture at  38 per kg. Find his gain per cent in the whole transaction.
Solution:
Total cost of rice of 1st variety = 36/kg × 20 kg = 720
Total cost of rice of 2nd variety = 32/kg × 25 kg = 800
Total cost of the two rice varieties = 720 + 800 = 1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = 38/kg × 45 kg = 1,710
Gain = SP - CP = 1,710 - 1,520 = 190
Gain% = 
Gain
CP
×100 % =
190
1520
×100 % = 12
1
2
%
Question:7
Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a  certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.
Solution:
Let 5 kg of coffee be mixed with 2 kg of chicory. CP of the mixture = Rs 250 ×5 +75 ×2 = Rs 1250 +150 = Rs. 1400SP of the mixture = Rs 7 ×230 = Rs. 1610Since SP > CP, there
Question:8
If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.
Solution:
Let Rs x be the SP of each bottle and Rs y be the CP of each bottle. SP of 16 bottles = CP of 17 bottles ? 16x = 17y ?
x
y
=
17
16
Gain per bottle = SP -CP = Rs x -y ? Gain percentage =
Question:9
The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.
Solution:
Let Rs x be the CP of one candle and Rs. y be the SP of one candle. Now, CP of 12 candles = SP of 15 candles ? 12x = 15y ?
y
x
=
12
15
Loss = CP -SP = Rs x -y ? Loss percentage =
Question:10
By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.
Solution:
It is given that,
Gain = SP of 5 cassettes                 .....1
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Page 3


Question:1
Find the gain or loss per cent when:
i
CP = Rs 620 and SP = Rs 713
ii
CP = Rs 675 and SP = Rs 630
iii
CP = Rs 345 and SP = Rs 372.60
iv
CP = Rs 80 and SP = Rs 76.80
Solution:
i CP = Rs. 620 SP = Rs. 713Since SP > CP, there is a gain. Gain = 713 - 620 = Rs. 93Gain percentage =
gain
CP
×100 %                              =
93
620
×100 %                               = 15 %
ii
CP = Rs 675 SP = Rs 630Since SP < CP, there is a loss. Loss = 675 - 630 = Rs. 45Loss percentage =
Loss
CP
×100 %               =
45
675
×100 %                = 6
2
3
%
iii
CP = Rs. 345 SP = Rs. 372. 60Since SP > CP, there is a gain. Gain = 372. 60 - 345 = Rs. 27. 6Gain percentage =
gain
CP
 ×100 %               =
27.6
345
×100 %                =
2760
345
%           
iv
CP = Rs 80 SP = Rs 76. 80Since SP < CP, there is a loss. Loss = 80 - 76. 80 = Rs. 3. 2Loss percentage =
loss
CP
 ×100 %                               =
3.2
80
×100 %                              =
32
80
×
Question:2
Find the selling price when:
i
CP = Rs 1650 and gain% = 4%
ii
CP = Rs 915 and gain% = 6
2
3
%
iii
CP = Rs 875 and loss% = 12%
iv
CP = Rs 645 and loss% = 13
1
3
%
Solution:
i
CP = Rs. 1650Gain percentage = 4 %SP =
(100+gain %)
100
×CP =
(100+4)
100
×1650 =
104×1650
100
= Rs. 1716
ii
CP = Rs. 915Gain percentage = 6
2
3
% =
20
3
%SP =
(100+gain %)
100
×CP =
100+
20
3
100
×915 =
320
3
100
×915 =
320
3
×
1
100
×915 = Rs. 976
iii
CP = Rs. 875Loss percentage = 12 %SP =
(100-loss %)
100
×CP =
(100-12)
100
×875 =
77000
100
= Rs. 770
iv
CP = Rs. 645Loss percentage = 13
1
3
% =
40
3
%SP =
(100-loss %)
100
×CP =
100-
40
3
100
×645 =
300-40
3
100
×645 =
260
3
×
1
100
×645 = Rs. 559
Question:3
Find the cost price when:
i
SP = Rs 1596 and gain% = 12%
ii
SP = Rs 2431 and loss% = 6
1
2
%
iii
SP = Rs 657.60 and loss% = 4%
iv
SP = Rs 34.40 and gain% = 7
1
2
%
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Solution:
i SP = Rs. 1596Gain percentage = 12 %CP =
100
(100+gain %)
×SP =
100
(100+12)
×1596 = Rs. 1425
ii
SP = Rs. 2431 Loss percentage = 6
1
2
% =
13
2
%CP =
100
(100-loss %)
×SP =
100
100-
13
2
×2431 =
100×2
187
×2431 = Rs. 2600
iii
SP = Rs. 657. 60 Loss percentage = 4 %CP =
100
(100-loss %)
×SP =
100
(100-4)
×657. 60 = Rs. 685
iv
SP = Rs. 34. 40 Gain percentage = 7
1
2
% =
15
2
%CP =
100
(100+gain %)
×SP =
100
100+
15
2
×34. 40 =
100×2
215
×34. 40 = Rs. 32
Question:4
Manjit bought an iron safe for  12160 and paid  340 for its transportation. Then, he sold it for  12875. Find his gain per cent
Solution:
CP of the iron safe = 12,160
Money spent on transportation = 340
Total CP = 12,160 + 340 = 12,500
SP of the iron safe = 12,875
Profit = SP - CP = 12,875 - 12,500 = 375
? Profit% = 
Profit
CP
×100 %
=
375
12500
×100 % = 3 %
 
Question:5
Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or
loss?
Solution:
CP of the car = Rs. 73500Repairs = Rs. 10300Insurance = Rs. 2600Total CP = 73500 +10300 +2600 = Rs. 86400SP = Rs. 84240Since SP < CP, Robin has a loss. Loss = 86400 -84240
Question:6
Hari bought 20 kg of rice at  36 per kg and 25 kg of rice at  32 per kg. He mixed the two varieties and sold the mixture at  38 per kg. Find his gain per cent in the whole transaction.
Solution:
Total cost of rice of 1st variety = 36/kg × 20 kg = 720
Total cost of rice of 2nd variety = 32/kg × 25 kg = 800
Total cost of the two rice varieties = 720 + 800 = 1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = 38/kg × 45 kg = 1,710
Gain = SP - CP = 1,710 - 1,520 = 190
Gain% = 
Gain
CP
×100 % =
190
1520
×100 % = 12
1
2
%
Question:7
Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a  certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.
Solution:
Let 5 kg of coffee be mixed with 2 kg of chicory. CP of the mixture = Rs 250 ×5 +75 ×2 = Rs 1250 +150 = Rs. 1400SP of the mixture = Rs 7 ×230 = Rs. 1610Since SP > CP, there
Question:8
If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.
Solution:
Let Rs x be the SP of each bottle and Rs y be the CP of each bottle. SP of 16 bottles = CP of 17 bottles ? 16x = 17y ?
x
y
=
17
16
Gain per bottle = SP -CP = Rs x -y ? Gain percentage =
Question:9
The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.
Solution:
Let Rs x be the CP of one candle and Rs. y be the SP of one candle. Now, CP of 12 candles = SP of 15 candles ? 12x = 15y ?
y
x
=
12
15
Loss = CP -SP = Rs x -y ? Loss percentage =
Question:10
By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.
Solution:
It is given that,
Gain = SP of 5 cassettes                 .....1
( )
( )
( )
( ) ( ) ( )
( )
( )
Gain = SP of 130 cassettes - CP of 130 cassettes
? SP of 5 cassettes = SP of 130 cassettes - CP of 130 cassettes              
From(1)
? CP of 130 cassettes = SP of 125 cassettes          .....2
Let the CP of 1 cassettte be x.
? CP of 125 cassettes = 125x
CP of 130 cassettes = 130x
SP of 125 cassettes = CP of 130 cassettes                   
From(2)
? SP of 125 cassettes = 130x
Now, gain% =
SP-CP
CP
×100 % =
(130x-125x)
125x
×100 %
=
5x
125x
×100 % = 4 %
Thus, the gain percent is 4%.  
Question:11
By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss per cent.
Solution:
Let Rs x be the SP of one lemon. SP of 45 lemons = Rs. 45xLoss = SP of 3 lemons = Rs. 3xBut loss = CP -SPCP = loss +SP = 3x +45x = Rs. 48x ? Loss percentage =
loss
CP
×100 % =
Question:12
Oranges are bought at 6 for  20 and sold at 4 for  18. Find the gain or loss per cent.
Solution:
LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = 20
So, CP of 1 orange = 
20
6
= 
10
3
CP of 12 orange = 12 ×
10
3
= 40
SP of 4 oranges = 18
SP of 1 orange = 
18
4
= 
9
2
SP of 12 oranges = 12 ×
9
2
= 54
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP - CP = 54 - 40 = 14
? Profit% = 
Profit
CP
×100 % =
14
40
×100 % = 35 %
Question:13
A vendor purchased bananas at  40 per dozen and sold them at 10 for  36. Find his gain or loss per cent.
Solution:
LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = 40
? CP of 1 banana = 
40
12
= 
10
3
? CP of 60 bananas = 60 ×
10
3
= 200
SP of 10 bananas = 36
? SP of 1 banana = 
36
10
= 
18
5
? SP of 60 bananas = 60 ×
18
5
= 216
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP - CP = 216 - 200 = 16
? Profit% = 
Profit
CP
×100 % =
16
200
×100 = 8 %
Question:14
A man bought apples at 10 for  75 and sold them at  75 per dozen. Find his loss per cent.
Solution:
LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = 75
? CP of 1 orange = 
75
10
? CP of 60 orange = 60 ×
75
10
= 450
SP of 12 oranges = 75
? SP of 1 orange = 
75
12
? SP of 60 oranges = 60 ×
75
12
= 375
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Page 4


Question:1
Find the gain or loss per cent when:
i
CP = Rs 620 and SP = Rs 713
ii
CP = Rs 675 and SP = Rs 630
iii
CP = Rs 345 and SP = Rs 372.60
iv
CP = Rs 80 and SP = Rs 76.80
Solution:
i CP = Rs. 620 SP = Rs. 713Since SP > CP, there is a gain. Gain = 713 - 620 = Rs. 93Gain percentage =
gain
CP
×100 %                              =
93
620
×100 %                               = 15 %
ii
CP = Rs 675 SP = Rs 630Since SP < CP, there is a loss. Loss = 675 - 630 = Rs. 45Loss percentage =
Loss
CP
×100 %               =
45
675
×100 %                = 6
2
3
%
iii
CP = Rs. 345 SP = Rs. 372. 60Since SP > CP, there is a gain. Gain = 372. 60 - 345 = Rs. 27. 6Gain percentage =
gain
CP
 ×100 %               =
27.6
345
×100 %                =
2760
345
%           
iv
CP = Rs 80 SP = Rs 76. 80Since SP < CP, there is a loss. Loss = 80 - 76. 80 = Rs. 3. 2Loss percentage =
loss
CP
 ×100 %                               =
3.2
80
×100 %                              =
32
80
×
Question:2
Find the selling price when:
i
CP = Rs 1650 and gain% = 4%
ii
CP = Rs 915 and gain% = 6
2
3
%
iii
CP = Rs 875 and loss% = 12%
iv
CP = Rs 645 and loss% = 13
1
3
%
Solution:
i
CP = Rs. 1650Gain percentage = 4 %SP =
(100+gain %)
100
×CP =
(100+4)
100
×1650 =
104×1650
100
= Rs. 1716
ii
CP = Rs. 915Gain percentage = 6
2
3
% =
20
3
%SP =
(100+gain %)
100
×CP =
100+
20
3
100
×915 =
320
3
100
×915 =
320
3
×
1
100
×915 = Rs. 976
iii
CP = Rs. 875Loss percentage = 12 %SP =
(100-loss %)
100
×CP =
(100-12)
100
×875 =
77000
100
= Rs. 770
iv
CP = Rs. 645Loss percentage = 13
1
3
% =
40
3
%SP =
(100-loss %)
100
×CP =
100-
40
3
100
×645 =
300-40
3
100
×645 =
260
3
×
1
100
×645 = Rs. 559
Question:3
Find the cost price when:
i
SP = Rs 1596 and gain% = 12%
ii
SP = Rs 2431 and loss% = 6
1
2
%
iii
SP = Rs 657.60 and loss% = 4%
iv
SP = Rs 34.40 and gain% = 7
1
2
%
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Solution:
i SP = Rs. 1596Gain percentage = 12 %CP =
100
(100+gain %)
×SP =
100
(100+12)
×1596 = Rs. 1425
ii
SP = Rs. 2431 Loss percentage = 6
1
2
% =
13
2
%CP =
100
(100-loss %)
×SP =
100
100-
13
2
×2431 =
100×2
187
×2431 = Rs. 2600
iii
SP = Rs. 657. 60 Loss percentage = 4 %CP =
100
(100-loss %)
×SP =
100
(100-4)
×657. 60 = Rs. 685
iv
SP = Rs. 34. 40 Gain percentage = 7
1
2
% =
15
2
%CP =
100
(100+gain %)
×SP =
100
100+
15
2
×34. 40 =
100×2
215
×34. 40 = Rs. 32
Question:4
Manjit bought an iron safe for  12160 and paid  340 for its transportation. Then, he sold it for  12875. Find his gain per cent
Solution:
CP of the iron safe = 12,160
Money spent on transportation = 340
Total CP = 12,160 + 340 = 12,500
SP of the iron safe = 12,875
Profit = SP - CP = 12,875 - 12,500 = 375
? Profit% = 
Profit
CP
×100 %
=
375
12500
×100 % = 3 %
 
Question:5
Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or
loss?
Solution:
CP of the car = Rs. 73500Repairs = Rs. 10300Insurance = Rs. 2600Total CP = 73500 +10300 +2600 = Rs. 86400SP = Rs. 84240Since SP < CP, Robin has a loss. Loss = 86400 -84240
Question:6
Hari bought 20 kg of rice at  36 per kg and 25 kg of rice at  32 per kg. He mixed the two varieties and sold the mixture at  38 per kg. Find his gain per cent in the whole transaction.
Solution:
Total cost of rice of 1st variety = 36/kg × 20 kg = 720
Total cost of rice of 2nd variety = 32/kg × 25 kg = 800
Total cost of the two rice varieties = 720 + 800 = 1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = 38/kg × 45 kg = 1,710
Gain = SP - CP = 1,710 - 1,520 = 190
Gain% = 
Gain
CP
×100 % =
190
1520
×100 % = 12
1
2
%
Question:7
Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a  certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.
Solution:
Let 5 kg of coffee be mixed with 2 kg of chicory. CP of the mixture = Rs 250 ×5 +75 ×2 = Rs 1250 +150 = Rs. 1400SP of the mixture = Rs 7 ×230 = Rs. 1610Since SP > CP, there
Question:8
If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.
Solution:
Let Rs x be the SP of each bottle and Rs y be the CP of each bottle. SP of 16 bottles = CP of 17 bottles ? 16x = 17y ?
x
y
=
17
16
Gain per bottle = SP -CP = Rs x -y ? Gain percentage =
Question:9
The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.
Solution:
Let Rs x be the CP of one candle and Rs. y be the SP of one candle. Now, CP of 12 candles = SP of 15 candles ? 12x = 15y ?
y
x
=
12
15
Loss = CP -SP = Rs x -y ? Loss percentage =
Question:10
By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.
Solution:
It is given that,
Gain = SP of 5 cassettes                 .....1
( )
( )
( )
( ) ( ) ( )
( )
( )
Gain = SP of 130 cassettes - CP of 130 cassettes
? SP of 5 cassettes = SP of 130 cassettes - CP of 130 cassettes              
From(1)
? CP of 130 cassettes = SP of 125 cassettes          .....2
Let the CP of 1 cassettte be x.
? CP of 125 cassettes = 125x
CP of 130 cassettes = 130x
SP of 125 cassettes = CP of 130 cassettes                   
From(2)
? SP of 125 cassettes = 130x
Now, gain% =
SP-CP
CP
×100 % =
(130x-125x)
125x
×100 %
=
5x
125x
×100 % = 4 %
Thus, the gain percent is 4%.  
Question:11
By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss per cent.
Solution:
Let Rs x be the SP of one lemon. SP of 45 lemons = Rs. 45xLoss = SP of 3 lemons = Rs. 3xBut loss = CP -SPCP = loss +SP = 3x +45x = Rs. 48x ? Loss percentage =
loss
CP
×100 % =
Question:12
Oranges are bought at 6 for  20 and sold at 4 for  18. Find the gain or loss per cent.
Solution:
LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = 20
So, CP of 1 orange = 
20
6
= 
10
3
CP of 12 orange = 12 ×
10
3
= 40
SP of 4 oranges = 18
SP of 1 orange = 
18
4
= 
9
2
SP of 12 oranges = 12 ×
9
2
= 54
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP - CP = 54 - 40 = 14
? Profit% = 
Profit
CP
×100 % =
14
40
×100 % = 35 %
Question:13
A vendor purchased bananas at  40 per dozen and sold them at 10 for  36. Find his gain or loss per cent.
Solution:
LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = 40
? CP of 1 banana = 
40
12
= 
10
3
? CP of 60 bananas = 60 ×
10
3
= 200
SP of 10 bananas = 36
? SP of 1 banana = 
36
10
= 
18
5
? SP of 60 bananas = 60 ×
18
5
= 216
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP - CP = 216 - 200 = 16
? Profit% = 
Profit
CP
×100 % =
16
200
×100 = 8 %
Question:14
A man bought apples at 10 for  75 and sold them at  75 per dozen. Find his loss per cent.
Solution:
LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = 75
? CP of 1 orange = 
75
10
? CP of 60 orange = 60 ×
75
10
= 450
SP of 12 oranges = 75
? SP of 1 orange = 
75
12
? SP of 60 oranges = 60 ×
75
12
= 375
( )
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP - SP = 450 - 375 = 75
? Loss% = 
Loss
CP
×100 % =
75
450
×100 % = 16
2
3
%
Question:15
A man purchased some eggs at 3 for  16 and sold them at 5 for  36. Thus, he gained  168 in all. How many eggs did he purchase?
Solution:
Let the number of eggs purchased be x.
CP of 3 eggs = 16
? CP of 1 egg = 
16
3
? CP of x eggs = 
16
3
x
SP of 5 eggs = 36
? SP of 1 egg = 
36
5
? SP of x eggs = 
36
5
x
Gain = SP - CP = 168
?
36
5
x -
16
3
x = 168 ?
28
15
x = 168 ? x =
168×15
28
? x = 90
Hence, the man purchased 90 eggs.
Question:16
A dealer sold a camera for Rs 1080 gaining 
1
8
of its cost price. Find i
the cost price of the camera, and ii
the gain per cent earned by the dealer.
Solution:
SP of the camera = Rs. 1080Let Rs x be the CP. Gain = Rs. 
1
8
x     . . . i Also, gain = SP -CP                   = Rs. 1080 -x      . . . ii From i and ii , we have:
1
8
x = 1080 -x ? x = 8640
Question:17
Meenakshi sells a pen for Rs 54 and loses 
1
10
of her outlay. Find i
the cost price of the pen, and ii
the loss per cent.
Solution:
SP of the pen = Rs. 54Let Rs x be the CP of the pen. Loss = Rs. 
x
10
SP = CP -Loss     = x -
x
10
    = Rs. 
9x
10
Now, we have
9x
10
= 54 ? x = 54 ×
10
9
? x = 60 ? CP of the pen = Rs. 60Now, loss =
Question:18
A dealer gets  940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.
Solution:
Let the cost price be x.
Loss = 10% of x = 
10
100
x = 
x
10
SP in case of loss = CP - Loss = x -
x
10
= 
9x
10
Gain =10% of x = 
10
100
x = 
x
10
SP in case of profit = CP + Profit = x +
x
10
= 
11x
10
It is given that dealer gets 940 more if sold at a profit of 10% instead of loss of 10%.
? SP in case of profit - SP in case of loss = 940
?
11x
10
-
9x
10
= 940 ?
2x
10
= 940 ? x = 4700
Hence, the cost price of the table is 4,700.
Question:19
A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.
Solution:
Let Rs x be the CP. Gain
1
 percentage =
gain 1
CP
×100 % ? 15 =
gain 1
x
×100 ? Gain
1
= Rs 
15x
100
Again, gain
2
 percentage =
gain 2
CP
×100 % ? 8 =
gain 2
x
×100 ? Gain
2
= Rs 
8x
100
According to the question
Question:20
A cycle was sold at a gain of 10%. Had it been sold for  260 more, the gain would have been 14%. Find the cost price of the cycle.
Solution:
Let the CP be x.
SP when gain is 10% = x +
10
100
x = 
110
100
x
SP when gain is 14% = x +
14
100
x = 
114
100
x
Difference in SP = SP when gain is 14% - SP when gain is 10% = 260
( ) ( ) ( ) ( ) ( )
( ) ( )
Page 5


Question:1
Find the gain or loss per cent when:
i
CP = Rs 620 and SP = Rs 713
ii
CP = Rs 675 and SP = Rs 630
iii
CP = Rs 345 and SP = Rs 372.60
iv
CP = Rs 80 and SP = Rs 76.80
Solution:
i CP = Rs. 620 SP = Rs. 713Since SP > CP, there is a gain. Gain = 713 - 620 = Rs. 93Gain percentage =
gain
CP
×100 %                              =
93
620
×100 %                               = 15 %
ii
CP = Rs 675 SP = Rs 630Since SP < CP, there is a loss. Loss = 675 - 630 = Rs. 45Loss percentage =
Loss
CP
×100 %               =
45
675
×100 %                = 6
2
3
%
iii
CP = Rs. 345 SP = Rs. 372. 60Since SP > CP, there is a gain. Gain = 372. 60 - 345 = Rs. 27. 6Gain percentage =
gain
CP
 ×100 %               =
27.6
345
×100 %                =
2760
345
%           
iv
CP = Rs 80 SP = Rs 76. 80Since SP < CP, there is a loss. Loss = 80 - 76. 80 = Rs. 3. 2Loss percentage =
loss
CP
 ×100 %                               =
3.2
80
×100 %                              =
32
80
×
Question:2
Find the selling price when:
i
CP = Rs 1650 and gain% = 4%
ii
CP = Rs 915 and gain% = 6
2
3
%
iii
CP = Rs 875 and loss% = 12%
iv
CP = Rs 645 and loss% = 13
1
3
%
Solution:
i
CP = Rs. 1650Gain percentage = 4 %SP =
(100+gain %)
100
×CP =
(100+4)
100
×1650 =
104×1650
100
= Rs. 1716
ii
CP = Rs. 915Gain percentage = 6
2
3
% =
20
3
%SP =
(100+gain %)
100
×CP =
100+
20
3
100
×915 =
320
3
100
×915 =
320
3
×
1
100
×915 = Rs. 976
iii
CP = Rs. 875Loss percentage = 12 %SP =
(100-loss %)
100
×CP =
(100-12)
100
×875 =
77000
100
= Rs. 770
iv
CP = Rs. 645Loss percentage = 13
1
3
% =
40
3
%SP =
(100-loss %)
100
×CP =
100-
40
3
100
×645 =
300-40
3
100
×645 =
260
3
×
1
100
×645 = Rs. 559
Question:3
Find the cost price when:
i
SP = Rs 1596 and gain% = 12%
ii
SP = Rs 2431 and loss% = 6
1
2
%
iii
SP = Rs 657.60 and loss% = 4%
iv
SP = Rs 34.40 and gain% = 7
1
2
%
( ) ( ) ( )
( ) ( )
( ) ( ) ( )
( ) ( ) (
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Solution:
i SP = Rs. 1596Gain percentage = 12 %CP =
100
(100+gain %)
×SP =
100
(100+12)
×1596 = Rs. 1425
ii
SP = Rs. 2431 Loss percentage = 6
1
2
% =
13
2
%CP =
100
(100-loss %)
×SP =
100
100-
13
2
×2431 =
100×2
187
×2431 = Rs. 2600
iii
SP = Rs. 657. 60 Loss percentage = 4 %CP =
100
(100-loss %)
×SP =
100
(100-4)
×657. 60 = Rs. 685
iv
SP = Rs. 34. 40 Gain percentage = 7
1
2
% =
15
2
%CP =
100
(100+gain %)
×SP =
100
100+
15
2
×34. 40 =
100×2
215
×34. 40 = Rs. 32
Question:4
Manjit bought an iron safe for  12160 and paid  340 for its transportation. Then, he sold it for  12875. Find his gain per cent
Solution:
CP of the iron safe = 12,160
Money spent on transportation = 340
Total CP = 12,160 + 340 = 12,500
SP of the iron safe = 12,875
Profit = SP - CP = 12,875 - 12,500 = 375
? Profit% = 
Profit
CP
×100 %
=
375
12500
×100 % = 3 %
 
Question:5
Robin purchased an old car for Rs 73500. He spent Rs 10300 on repairs and paid Rs 2600 for its insurance. Then he sold it to a mechanic for Rs 84240. What was his percentage gain or
loss?
Solution:
CP of the car = Rs. 73500Repairs = Rs. 10300Insurance = Rs. 2600Total CP = 73500 +10300 +2600 = Rs. 86400SP = Rs. 84240Since SP < CP, Robin has a loss. Loss = 86400 -84240
Question:6
Hari bought 20 kg of rice at  36 per kg and 25 kg of rice at  32 per kg. He mixed the two varieties and sold the mixture at  38 per kg. Find his gain per cent in the whole transaction.
Solution:
Total cost of rice of 1st variety = 36/kg × 20 kg = 720
Total cost of rice of 2nd variety = 32/kg × 25 kg = 800
Total cost of the two rice varieties = 720 + 800 = 1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = 38/kg × 45 kg = 1,710
Gain = SP - CP = 1,710 - 1,520 = 190
Gain% = 
Gain
CP
×100 % =
190
1520
×100 % = 12
1
2
%
Question:7
Coffee costing Rs 250 per kg was mixed with chicory costing Rs 75 per kg in the ratio 5 : 2 for a  certain blend. If the mixture was sold at Rs 230 per kg, find the gain or loss per cent.
Solution:
Let 5 kg of coffee be mixed with 2 kg of chicory. CP of the mixture = Rs 250 ×5 +75 ×2 = Rs 1250 +150 = Rs. 1400SP of the mixture = Rs 7 ×230 = Rs. 1610Since SP > CP, there
Question:8
If the selling price of 16 water bottles is equal to the cost price of 17 water bottles, find the gain per cent earned by the dealer.
Solution:
Let Rs x be the SP of each bottle and Rs y be the CP of each bottle. SP of 16 bottles = CP of 17 bottles ? 16x = 17y ?
x
y
=
17
16
Gain per bottle = SP -CP = Rs x -y ? Gain percentage =
Question:9
The cost price of 12 candles is equal to the selling price of 15 candles. Find the loss per cent.
Solution:
Let Rs x be the CP of one candle and Rs. y be the SP of one candle. Now, CP of 12 candles = SP of 15 candles ? 12x = 15y ?
y
x
=
12
15
Loss = CP -SP = Rs x -y ? Loss percentage =
Question:10
By selling 130 cassettes, a man gains an amount equal to the selling price of 5 cassettes. Find the gain per cent.
Solution:
It is given that,
Gain = SP of 5 cassettes                 .....1
( )
( )
( )
( ) ( ) ( )
( )
( )
Gain = SP of 130 cassettes - CP of 130 cassettes
? SP of 5 cassettes = SP of 130 cassettes - CP of 130 cassettes              
From(1)
? CP of 130 cassettes = SP of 125 cassettes          .....2
Let the CP of 1 cassettte be x.
? CP of 125 cassettes = 125x
CP of 130 cassettes = 130x
SP of 125 cassettes = CP of 130 cassettes                   
From(2)
? SP of 125 cassettes = 130x
Now, gain% =
SP-CP
CP
×100 % =
(130x-125x)
125x
×100 %
=
5x
125x
×100 % = 4 %
Thus, the gain percent is 4%.  
Question:11
By selling 45 lemons, a vendor loses a sum equal to the selling price of 3 lemons. Find his loss per cent.
Solution:
Let Rs x be the SP of one lemon. SP of 45 lemons = Rs. 45xLoss = SP of 3 lemons = Rs. 3xBut loss = CP -SPCP = loss +SP = 3x +45x = Rs. 48x ? Loss percentage =
loss
CP
×100 % =
Question:12
Oranges are bought at 6 for  20 and sold at 4 for  18. Find the gain or loss per cent.
Solution:
LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = 20
So, CP of 1 orange = 
20
6
= 
10
3
CP of 12 orange = 12 ×
10
3
= 40
SP of 4 oranges = 18
SP of 1 orange = 
18
4
= 
9
2
SP of 12 oranges = 12 ×
9
2
= 54
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP - CP = 54 - 40 = 14
? Profit% = 
Profit
CP
×100 % =
14
40
×100 % = 35 %
Question:13
A vendor purchased bananas at  40 per dozen and sold them at 10 for  36. Find his gain or loss per cent.
Solution:
LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = 40
? CP of 1 banana = 
40
12
= 
10
3
? CP of 60 bananas = 60 ×
10
3
= 200
SP of 10 bananas = 36
? SP of 1 banana = 
36
10
= 
18
5
? SP of 60 bananas = 60 ×
18
5
= 216
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP - CP = 216 - 200 = 16
? Profit% = 
Profit
CP
×100 % =
16
200
×100 = 8 %
Question:14
A man bought apples at 10 for  75 and sold them at  75 per dozen. Find his loss per cent.
Solution:
LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = 75
? CP of 1 orange = 
75
10
? CP of 60 orange = 60 ×
75
10
= 450
SP of 12 oranges = 75
? SP of 1 orange = 
75
12
? SP of 60 oranges = 60 ×
75
12
= 375
( )
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP - SP = 450 - 375 = 75
? Loss% = 
Loss
CP
×100 % =
75
450
×100 % = 16
2
3
%
Question:15
A man purchased some eggs at 3 for  16 and sold them at 5 for  36. Thus, he gained  168 in all. How many eggs did he purchase?
Solution:
Let the number of eggs purchased be x.
CP of 3 eggs = 16
? CP of 1 egg = 
16
3
? CP of x eggs = 
16
3
x
SP of 5 eggs = 36
? SP of 1 egg = 
36
5
? SP of x eggs = 
36
5
x
Gain = SP - CP = 168
?
36
5
x -
16
3
x = 168 ?
28
15
x = 168 ? x =
168×15
28
? x = 90
Hence, the man purchased 90 eggs.
Question:16
A dealer sold a camera for Rs 1080 gaining 
1
8
of its cost price. Find i
the cost price of the camera, and ii
the gain per cent earned by the dealer.
Solution:
SP of the camera = Rs. 1080Let Rs x be the CP. Gain = Rs. 
1
8
x     . . . i Also, gain = SP -CP                   = Rs. 1080 -x      . . . ii From i and ii , we have:
1
8
x = 1080 -x ? x = 8640
Question:17
Meenakshi sells a pen for Rs 54 and loses 
1
10
of her outlay. Find i
the cost price of the pen, and ii
the loss per cent.
Solution:
SP of the pen = Rs. 54Let Rs x be the CP of the pen. Loss = Rs. 
x
10
SP = CP -Loss     = x -
x
10
    = Rs. 
9x
10
Now, we have
9x
10
= 54 ? x = 54 ×
10
9
? x = 60 ? CP of the pen = Rs. 60Now, loss =
Question:18
A dealer gets  940 more if instead of selling a table at a loss of 10%, it is sold at a gain of 10%. Find the cost price of the table.
Solution:
Let the cost price be x.
Loss = 10% of x = 
10
100
x = 
x
10
SP in case of loss = CP - Loss = x -
x
10
= 
9x
10
Gain =10% of x = 
10
100
x = 
x
10
SP in case of profit = CP + Profit = x +
x
10
= 
11x
10
It is given that dealer gets 940 more if sold at a profit of 10% instead of loss of 10%.
? SP in case of profit - SP in case of loss = 940
?
11x
10
-
9x
10
= 940 ?
2x
10
= 940 ? x = 4700
Hence, the cost price of the table is 4,700.
Question:19
A dealer gets Rs 56 less if instead of selling a chair at a gain of 15%, it is sold at a gain of 8%. Find the cost price of the chair.
Solution:
Let Rs x be the CP. Gain
1
 percentage =
gain 1
CP
×100 % ? 15 =
gain 1
x
×100 ? Gain
1
= Rs 
15x
100
Again, gain
2
 percentage =
gain 2
CP
×100 % ? 8 =
gain 2
x
×100 ? Gain
2
= Rs 
8x
100
According to the question
Question:20
A cycle was sold at a gain of 10%. Had it been sold for  260 more, the gain would have been 14%. Find the cost price of the cycle.
Solution:
Let the CP be x.
SP when gain is 10% = x +
10
100
x = 
110
100
x
SP when gain is 14% = x +
14
100
x = 
114
100
x
Difference in SP = SP when gain is 14% - SP when gain is 10% = 260
( ) ( ) ( ) ( ) ( )
( ) ( )
?
114x
100
-
110x
100
= 260 ?
4x
100
= 260 ? x = 6500
Hence, the CP of the cycle is 6,500.
Question:21
Sonu buys 40 kg of wheat at  12.50 per kg and 30 kg of wheat at  14 per kg. At what rate per kg should he sell the mixture to gain 5% on the whole?
Solution:
40 kg of wheat is bought for 12.50/kg.
? CP of 40 kg of wheat = 40 × 12.50 = 500
30 kg of wheat is bought for 14/kg.
? CP of 30 kg of wheat = 30 × 14 = 420
Total CP = 500 + 420 = 920
Profit = 5% of CP = 5% of 920 = 
5
100
×920 = 46
Let the SP be x.
Profit = SP - CP
? x - 920 = 46
? x = 966
SP of 70 kg wheat = 966
? SP of 1 kg wheat = 
966
70
= 13. 80
Thus, the selling price of the mixture is 13.80/kg.
Question:22
Wasim bought two cricket bats for  840 and  360 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss per cent in the whole
transaction.
Solution:
CP of the first bat = 840
Profit% on the first bat = 15%
? Profit = 15% of 840 = 
15
100
×840 = 126
SP of the first bat = 840 + 126 = 966
CP of the second bat = 360
Loss = 5% of 360 = 
5
100
×360 = 18
SP of the second bat = 360 - 18 = 342
Total CP of two bats = CP of first bat + CP of second bat = 840 + 360 = 1,200
Total SP of two bats = SP of first bat + SP of second bat = 966 + 342 = 1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats - Total CP of two bats = 1,308 - 1,200 = 108
? Gain% in the whole transaction =
Gain
Total CP of two bats
×100 %
=
108
1200
×100 = 9 %
Question:23
Hema bought two pairs of jeans for  1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss per cent in the whole transaction.
Solution:
CP of first jeans = 1,450
Profit = 8% of CP = 
8
100
×1450 = 116
SP of first jeans = 1,450 + 116 = 1,566
CP of second jeans = 1,450
Loss = 4% of CP = 
4
100
×1450 = 58
SP of second jeans = 1450 - 58 = 1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = 1,450 + 1,450 = 2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = 1,566 + 1,392 = 2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans - Total CP of two jeans = 2,958 - 2,900 = 58
? Gain% = 
Gain
Total CP of two jeans
×100 % =
58
2900
×100 % = 2 %
Question:24
A grocer purchased 200 kg of rice at Rs 25 per kg. He sold 80 kg of it at a gain of 10% and 40 kg at a loss of 4%. At what rate per kg should he sell the remainder to gain 8% on his total
investment?
Solution:
CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= Rs (200 ×25) = Rs 5000
CP of 80 kg of rice=Rs (25 ×80) = Rs 2000
CP of 40 kg of rice = Rs (25 ×40) = Rs 1000
 
SP of 80 kg of rice = 
100+gain%
100
×CP = Rs 
110
100
×2000 = Rs 2200
SP of 40 kg rice =
100-loss%
100
×CP = Rs 
96
100
×1000 = Rs 960
 SP of 200 kg rice =
100+gain%
100
×CP = Rs 
108
100
×5000 = Rs 5400