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Profit and Loss Class 8 RS Aggarwal Exe-7A Goyal Brothers ICSE Maths Solutions
| Board | ICSE |
| Publications | Goyal Brothers Prakshan |
| Subject | Maths |
| Class | 8th |
| writer | RS Aggarwal |
| Book Name | Foundation |
| Ch-7 | Profit and Loss Discount Tax |
| Exe-7A | Gain and Loss Percent |
| Edition | 2024-2025 |
How to Calculate Gain or Loss Percent
The formula to calculate the profit percentage and Loss Percentage is given below:
- Profit % = (Profit/Cost Price) × 100.
- Loss % =( Loss/Cost Price) × 100
Exercise- 7A
(Profit and Loss Discount Tax Class 8 RS Aggarwal Exe-7A Goyal Brothers ICSE Maths Solutions)
Que-1: Find the gain or loss per cent, when :
(i) C.P. = Rs750, S.P. = Rs875 (ii) C.P. = Rs126, S.P. = Rs94.50, (iii) C.P. = Rs80.40, S.P. = Rs68.34 (iv) C.P. = Rs58.75, S.P. = Rs51.70
Sol: (i) CP is smaller than SP so there is a gain here
Gain = SP – CP = 875 – 750 = 125
Gain % = (Gain × 100) ÷ CP
= (125 ×100 ) ÷ 750
= 12500 ÷ 750
= 50/3
= 16*(2/3)%
(ii) CP is greater than SP so there is a loss here
Loss = CP – SP = 126 – 94.50 = 31.50
Loss % = (Loss × 100) ÷ CP
= (31.50 ×100 ) ÷ 126
= 3150 ÷ 126
= 25%
(iii) CP is greater than SP so there is a loss here
Loss = CP – SP = 80.40 – 68.34 = 12.06
Loss % = (Loss × 100) ÷ CP
= (12.06 ×100 ) ÷ 80.40
= 1206 ÷ 80.40
= 15%
(iv) CP is greater than SP so there is a loss here
Loss = CP – SP = 58.75 – 51.70 = 7.05
Loss % = (Loss × 100) ÷ CP
= (7.05×100 ) ÷ 58.75
= 705 ÷ 58.75
= 12%
Que-2: Ranjit purchased an almirah for Rs5248 and paid Rs127 for its transportation. He sold it for Rs6020. Find his gain or loss per cent.
Sol: Total cost price = 5248+127
= 5375
Selling price = 6020
Gain = {(SP−CP)/CP} × 100 = {(6020−5375)/5375} × 100
= 12% gain
Que-3: Ahmed purchased an old scooter for Rs14625 and spent Rs3225 on its repair. Then, he sold it for Rs16422. Find his gain or loss per cent.
Sol: Total cost price (including repairs) = 14625+3225
= 17850
Selling price = 16422.
loss = {(CP−S.P)/C.P} × 100 = {(17850−16422)/17850} × 100
= 8% loss.
Que-4: A man buys two cricket bats, one for Rs1360 and the other for Rs1040. He sells the first bat at a gain of 15% and the second one at the loss of 15%. Find his gain or loss per cent in the whole transaction.
Sol: For 1st bat
Cost prize = Rs1360
Gain = (15/100) × 1360 = Rs204
Selling prize = 1360+204 = Rs1564
For 2nd bat
Cost prize = Rs1040
Loss = (15/100) × 1040 = Rs156
Selling prize = 1040−156 = Rs884
Total Cost prize = 1360+1040 = Rs2400
Total Selling prize = 1564+884 = Rs2448
Gain = 2448−2400 = Rs48
Percentage gain = (48/2400) × 100 = 2%
Que-5: Nandlal bought 20 dozen notebooks at Rs156 per dozen. He sold 8 dozens of them at 10% gain and the remaining 12 dozen at 20% gain. What is his gain per cent in the whole transaction.
Sol: Nandlal bought 20 dozen Notebooks at Rs.156 per dozen
Total purchasing price = 156×20
= 3120
He sold 8 dozen at 10% profit + 12 dozen at 20% profit
[156×8+(156×8×10)/100] + [156×12+(156×12×20)/100]
⇒ 1248 + (1248/10) + 1872 + (3744/10)
⇒ (3120 + 1248 + 3744)/10
⇒ 3619.20
So selling price = 3619.2
profit = selling price – purchasing price
= 3619.2 − 3120
= 499.2
profit %= (499.2×100)/3120
= 16% Ans
Que-6: Heera bought 25 kg of rice at Rs48 per kg and 35 kg of rice at Rs60 per kg. He sold the mixture at Rs66 per kg. Find his gain per cent.
Sol: Total cost price (C.P)
= (25×48) + (35×60)
= 100×12 + 2100
= 3300
Total selling price(S.P)
= 66×(25+35)
= 66×60 = 3960
⇒ Profit percentage
= {(S.P−C.P)/C.P} × 100
= {(3960−3300)/3300} × 100
= (660/3300) × 100 = 20%
Que-7: If the selling price of an article is 4/5th of its cost price, find the loss per cent.
Sol: Let the cost price be x.
Then, selling price: 4x/5
Loss = C.P.-S.P. = x−(4x/5) = 1x/5
Loss percent = (Loss/Cost Price) × 100%
= {(x/5)/x} × 100%
= 1/5 × 100%
= 20%
Que-8: If the selling price of an article is 1*(1/3) of its cost price, find the gain per cent.
Sol: Let CP = 1
SP = 1*(1/3) = 4/3
Profit = 4/3 – 1 = 1/3.
So % profit = (1/3) *100 = 33*(1/3)%
Que-9: A man sold a table for Rs2250 and gained one-ninth of its cost price. Find : (i) the cost price of the table (ii) the gain per cent earned by the man.
Sol: S.P. of table = 2250 Rs.
Let the C.P. = x Rs.
gained 1/9 of cp
Gain = SP – CP
Therefore x + 1/9x = 2250
take lcm , (9x + x)/9
10x/9 = 2250
10x = 2250 x 9
X = (2250 x 9)/10
(i) X (C.P) = 2025
(ii) gain % = {(2250 – 2025)/2025} x 100
= (225/2025) x 100
= 100/9 = 11*(1/9)%.
Que-10: By selling a pen for Rs195, a man loses one-sixteenth of what it costs him. Find : (i) the cost price of the pen (ii) loss per cent
Sol: S.P. = Rs195
C.P. = x
Loss = x/16
Loss = C.P. – S.P.
x/16 = x – 195
x – (x/16) = 195
(16x-x)16 = 195
15x = 195 x 16
x = (195×16)/15
x = 208
(i) C.P. = x = Rs208.
(ii) Loss% = (loss/C.P.) x 100
= {(208/16)/208} x 100
= (13/208) x 100
= 25/4 = 6*(1/4)%.
Que-11: A cycle has sold at a gain of 10%. Had it been sold for Rs99 more, the gain would have been 12%. Find the cost price of the cycle.
Sol: Let the cost price of the cycle = ‘x’.
Given Gain = 10%.
We know that Selling price = [(100 + Gain%)/100] * CP
= [(100 + 10)/100] * x
= [110/100] * x
= 110x/100
= 11x/10.
Given that it had been sold for rs.99 more.
Selling price = (11x/10) + 99 —— (1)
Given the gain would have been 12%.
= Selling price = [(100 + Gain%)/100] * CP
= (112/100) * x
= 112x/100
= 28x/25 —— (2)
On solving (1) & (2), we get
= > (28x/25) = (11x/10) + 99
= > (28x/25) – (11x/10) = 99
= > (56x – 55x) = 99 * 50
= > x = 4950.
Que-12: A bucket was sold at a loss of 8%. Had it been sold for Rs56 more, there would have been a gain of 8%. What is the cost price of the bucket.
Sol: Loss = 8%
Let the cost price be x
SP = (100-8) × (x/100)
= 92x/100
SP = (92x/100) + 56
Gain% = 8%
SP = (100+8) × (x/100)
Difference between two SPs = 56
(108x/100) – (92x/100) = 56
16x = 56×100
x = (56×100)/16
x = 350
Que-13: The selling price of 18 books is equal to the cost price of 21 books. Find the gain or loss per cent.
Sol: Let the cost price of 21 books be a
Cost price of one book = a/21
Selling price of 18 book = a
=> Selling price of 1 book = a / 18
Gain on one book = SP – CP
= a/18 – a/21
= ( 7a – 6a) / 126
= a / 126.
Now,
Gain % = Gain on 1 book × 100 / CP of 1 book
= ( a / 126) × 100 / ( a / 21)
= 100 × 21 / 126
= 100/6
= 50/3 = 16*(2/3)%
Que-14: The cost price of 12 fans is equal to the selling price of 16 fans. Find his gain or loss per cent.
Sol: Let the cost price of 12 fans be a
Selling price of 16 fans = a
Cost price of one fan = a / 12
Selling price of one fan = a/16
Loss on one fan = CP – SP
= a/12 – a/16
= ( 4a – 3a) /48
= a / 48
Loss percent = Loss × 100 / CP
= ( a /48) × 100 / (a / 12)
= 100 /4
= 25 %
Que-15: On selling 250 cassettes, a man had a gain equal to the selling price of 25 cassettes. Find his gain per cent.
Sol: Gain = Selling price – Cost price
i.e. Gain = Selling price of 250 cassettes – Cost price of 250 cassettes
We have given,
Gain = Selling price of 25 cassettes
So, Selling price of 25 cassettes = Cost price of 250 cassettes
Let the cost price of 1 cassettes be Rs. ‘x’.
Cost price of 225 cassettes = Rs.225x
Selling price of 225 cassettes = Rs.250x
G% = {(SP-CP)/CP} x 100
G% = {(250x-225x)/225x} x 100
G% = (25x/225x) x 100
G% = 100/9 = 11*(1/9)%.
Que-16: On selling 36 oranges, a vendor losses the selling price of 4 oranges. Find his loss per cent.
Sol: Let SP of one orange = Rs1
SP of 36 oranges = Rs.36
Loss on 36 oranges = Rs.4
CP of 36 oranges = SP + Loss = 36+4 = 40
Thus, Loss % = (4/40)×100 = 10%
Que-17: Toffees are bought at 2 for a rupee and sold at 5 for Rs3. Find the gain or loss per cent.
Sol: 2 toffees = ₹ 1
1 toffee = 1/2 = ₹ 0.5
5 toffees = ₹ 3
1 toffee = 3/5 = ₹ 0.6.
CP = ₹ 0.5 and SP = ₹ 0.6
Hence, SP is more so Gain occurred.
Gain = SP – CP
Gain = 0.6 – 0.5
Gain = 0.1.
Gain percentage = (Gain/CP) x 100
Gain Percentage = (0.1/0.5) x 100
Gain Percentage = 20 %
Que-18: Coffee costing Rs450 per kg was mixed with Chicory costing Rs225 per kg in the ratio 5:2 for a certain blend. If the mixture was sold at Rs405 per kg; find the gain or loss per cent.
Sol: Given coffee cost = 450 per kg
Chicory cost = 225 per kg
Let coffee = 5x kg & chicory = 2x kg [coffee/chicory = 5/2]
Total cost = 5x+450+(2x×225) = 2700x.
Selling price = 7x × 405 = 2835x
S.P > C.P
∴ It’s profit
Profit percentage = (Profit/C.P) × 100 = {(2835x−2700x)/2700x} × 100
= (135x/2700x) x 100
= 5%.
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