08: Profit, Loss And Discount Class 8 Maths : Icse-viii-mathematics

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ICSE-VIII-Mathematics

08: Profit, Loss and Discount Class 8 Maths

with Solutions - page 2

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#7-ii
the cost price of the goods
Ans : C.P. = Rs. 5,500 + Rs. 550
= Rs. 6,050

#7-iii
the loss as percent.
Ans : Loss% = (550 × 100)/6050
= (10 × 100)/110
= 100/11
= 9 1/11%

Qstn #8
The selling price of a sofa-set is times of its cost price. Find the gain or the loss as percent.
Ans : Let the cost price (C.P.) = 1
S.P. = 1 × 4/5 = 4/5
∴ Loss = 1 - 4/5
= (5 - 4)/5
= 1/5 [∵ Loss = C.P. - S.P.]
∴ Loss% = Loss/C.P. = (1/5)/1 × 100
= 1/5 × 100
= 20%

Qstn #9
The cost price of an article is times of its selling price. Find the loss or the gain as percent.
Ans : Let S.P. = 1
C.P. = 4/5 × 1 = 4/5
∴ Gain = S.P. - C.P. [∵ Gain = S.P. - C.P.]
= 1 - 4/5
= (5 - 4)/5
= 1/5
∴ Gain % = Gain/C.P. × 100
= (1/5)/(4/5) × 100
= (1/5)/( 4/5) × 100
= 1/5 × 5/4 × 100
= 25%

Qstn #10
A shopkeeper sells his goods at 80% of their cost price. Find the percent gain or loses?
Ans : Let C.P. of goods = Rs. 100
∴ S.P. of goods = 80/100 × 100
= Rs. 80
Loss = C.P. - S.P.
= Rs. 100 - Rs. 80
= Rs. 20
Loss% = Loss/C.P. × 100
= 20/100 × 100
= 20%

Qstn #11
The cost price of an article is 90% of its selling price. What is the profit or the loss as percent?
Ans : Let S.P. of the article = Rs. 100
∴ C.P. of the article = 90/100 × 100
= Rs. 90
Gain = Rs. 100 - Rs. 90
= Rs. 10
Gain % = Gain/C.P. × 100
= 10/90 × 100
= 100/9 %
= 11 1/9%

Qstn #12
The cost price of an article is 30 percent less than its selling price. Find, the profit or loss as percent.
Ans : Let S.P. of the article = Rs. 100
30% of S.P. = Rs. 30/100 × 100
= Rs. 30
∴ C.P. of the article = 100 - 30 = Rs. 70
Profit = S.P. - C.P.
Rs. 100 - Rs. 70
= Rs. 30
Profit% = Profit/C.P. × 100
= 30/70 × 100
= 300/7%
= 42 6/7%

Qstn #13
A shop-keeper bought 300 eggs at 80 paisa each. 30 eggs were broken in transaction and then he sold the remaining eggs at one rupee each. Find, his gain or loss as percent.
Ans : C.P. of 300 egg@ 80 paise each = 300 × 80
= 24000 paise
= Rs. 240
No. of eggs which were broken in transaction = 30
Remaining eggs = 300 - 30
= 270
S.P. of eggs @ Rs. 1 each = 270 × 1
= Rs. 270
Gain = S.P. - C.P.
= Rs. 270 - Rs. 240
= Rs. 30
Gain % = Gain/C.P. × 100
= 30/240 × 100
= 100/8 %
= 12.5%

Qstn #14
A man sold his bicycle for Rs.405 losing one-tenth of its cost price, find :

#14-i
its cc price;
Ans : Let C.P. of the bicycle = Rs. x
∴ Loss = Rs. x/10
S.P. = C.P. - Loss
= x - x/10
But, we are given S.P. = Rs. 405
∴ x - x/10 = 405
⇒ (10x - x)/10 = 405
⇒ 9x/10 = 405⇒ x = 405 × 10/9
⇒ x = 4050/9⇒ x = 450
∴ C.P. = Rs. 450

#14-ii
the loss percent.
Ans : Loss = x/10
= 450/10 ...(Substituting the value of x)
= Rs. 45
Loss % = Loss/C.P. × 100
= 45/450 × 100
= 4500/450 = 10 %

Qstn #15
A man sold a radio-set for Rs.250 and gained one-ninth of its cost price. Find ;

#15-i
its cost price;
Ans : Let C.P. of the radio-set = Rs. x
Gain = Rs. x/9
S.P. = Rs. (x + x/9) = Rs.(9x + x)/9 = Rs. 10x/9
But, we are given S.P. of the radio-set = Rs. 250
∴ 10x/9 = 250
⇒ x = 250 × 9/10⇒ x = 25 × 9⇒ x = 225
∴ C.P. of the radio set = Rs.225

#15-ii
the profit percent.
Ans : Profit = Rs. x/9
= Rs. 225/9 ...(Substituting the value of x)
= Rs. 25
Profit% = Profit/C.P. × 100
= 25/225 × 100
= (25 × 100)/225
= 100/9%
= 11 1/9%

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Section : B