CONCEPT AND TRICKS ON PROFIT AND LOSS:
Cost Price-The price at which an article is purchased is called its cost price (C.P.)
Selling Price-The price at which the article is sold is called its selling price (S.P.)
1.If the cost price (C.P.) of the article is equal to the selling price (S.P.), Then there is no loss or gain.
2.If the selling price (S.P.) > cost price (C.P.), then the seller is said to have a profit or gain,
Gain or Profit = S.P. - C.P.
3.If the cost price (C.P.) > selling price (S.P.), then the seller is said to have a loss,
Loss = C.P. - S.P.
4. Gain% = {(Gain*100)/C.P.}
5. Loss% ={(Loss*100)/C.P.}
6. S.P. = {(100+Gain%)/100 * C.P.}
7. S.P. = {(100 - Loss%)/100 * C.P.}
8. C.P. = {(100/(100+Gain%) * S.P.}
9.C.P. = {(100/(100 - Loss%) * S.P.}
10. If an article is sold at a profit/gain of 30%, then S.P. = 130% of the C.P.
11. If an article is sold at a loss of 20%, then S.P. = 80% of the C.P.
12. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given by:
{x^2/100}%
13. A single discount equivalent to discount series of x% and y% given by the seller is equal to
{x +y - xy/100}%
14. If a trader professes to sell his goods at cost price, but uses false weights, then
Gain% = {Error/(True value - Error) x 100}%
Some Questions based on above concept and Tricks:
1.A trader sells two articles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two articles is Rs. 30, 000, find the difference between their cost prices:
(a) Rs. 5000
(b)Rs. 6000
(c) Rs. 7500
(d) None of these
2.60% goods are sold at 5% loss while rest are sold at 10% profit. If there is a total profit of Rs. 100, then the worth of goods sold it:
(a) Rs. 7500
(b) Rs. 5000
(c) Rs. 10000
(d) None of these
3.Two articles are sold at the same price. One at a profit of 75% and another one at a loss of 30%. What is the overall profit or loss?
(a) 22.5% profit
(b) 57.5 profit
(c) 13 2/7 % loss
(d) None of these
4.Mr. Mittal purchased a car for Rs. 3, 00, 000 and a bike for his son for Rs. 1, 00, 000. He sold the car at a profit of 10% and bike at a loss of 20%. What is the net gain or loss?
(a) 2% gain
(b) 1.5% loss
(c) 2.5 loss
(d) 2.5% gains
5.The profit percentage on the three articles A, B and C is 10% 20% and 25% and the ratio of the cost price is 1 : 2 : 4 . Also the ratio of number of articles sold of A, B and C is 2 : 5 : 2, then the overall profit percentage is:
(a) 18. 5%
(b) 21%
(c) 75%
(d) None of these
6.A single discount equivalent to three successive discounts of 5%, 10%, 20% is :
(a) 68. 4%
(b) 35%
(c) 31.6%
(d) 32%
7.On selling an article for Rs. 240, a trader loses 4%. In order to gain 10% he must sell that article for :
(a) Rs. 275
(b)Rs. 340
(c) Rs. 320
(d) Rs.264
8.6% more is gained by selling a coat for Rs. 1425 than by selling it for Rs. 1353. The cost price of the coat is :
(a) Rs. 1000
(b)Rs. 1250
(c) Rs.1500
(d)Rs. 1200
9.ITC sells one product at a profit of 20% another at a loss 20% at the same selling price. What is the loss incurred by ITC?
(a) 1 %
(b) 2 %
(c) 4%
(d) 0%
10.Each of A and B sold their article at Rs. 1818 but A incurred a loss of 10% while B gained by 1%. What is the ratio of cost price of the articles of A to that of B?
(a) 101 : 90
(b) 85 : 89
(c) 81 : 75
(d) None of these
ANSWERS AND SOLUTION :
1.(b)
10% x = 15% of y, where x + y = 30000
=> x/y = 3k/2k
Hence, the difference = k = 6000
2.(c)
SP of 60% goods=0.6y × 0.95=0.57y
} Total SP =1.01y
SP of 40% goods=0.4y × 1.1=0.44y
Profit = 0.01y = 100
y = 10000
3.(d)
4.(d)
Gain = 30000
Loss = 20000
Net gain = 10000 over Rs. 4 lakh
Hence, profit = 10000/400000 * 100 = 2.5%
5.(b)
CP of A + B + C = 2x * y + 5x * 2y + 2x + 4y = 20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total Profit = 4.2xy
% profit = 4.2xy/20xy * 100 = 21%
6.(c)
Reduced price = 100 * 0.95 * 0.90 * 0.80 = 68.40
so Single discount = (100 – 68.4)% = 31. 6%
7.(a)
Let the CP be Rs. x, then SP be 0.96x
so 0.96x = 240
X = 250
Now the new SP = 250 * 1.1 = 275
8.(d) 1435 – 1353 = 72 = 6% of CP
=> CP = 1200
9.(c)
Loss % = ((common gain or loss)/10)^2 %
= (20/10)^2 % = 4%
10.(a)
CP of A = 1818/0.9 = 2020
CP of B = 1818/1.01 = 1800
CP of A/CP of B = 2020/1800 = 101/90
1.(b)
10% x = 15% of y, where x + y = 30000
=> x/y = 3k/2k
Hence, the difference = k = 6000
2.(c)
SP of 60% goods=0.6y × 0.95=0.57y
} Total SP =1.01y
SP of 40% goods=0.4y × 1.1=0.44y
Profit = 0.01y = 100
y = 10000
3.(d)
4.(d)
Gain = 30000
Loss = 20000
Net gain = 10000 over Rs. 4 lakh
Hence, profit = 10000/400000 * 100 = 2.5%
5.(b)
CP of A + B + C = 2x * y + 5x * 2y + 2x + 4y = 20xy
Profit of A = 0.2xy
Profit of B = 2xy
Profit of C = 2xy
Total Profit = 4.2xy
% profit = 4.2xy/20xy * 100 = 21%
6.(c)
Reduced price = 100 * 0.95 * 0.90 * 0.80 = 68.40
so Single discount = (100 – 68.4)% = 31. 6%
7.(a)
Let the CP be Rs. x, then SP be 0.96x
so 0.96x = 240
X = 250
Now the new SP = 250 * 1.1 = 275
8.(d) 1435 – 1353 = 72 = 6% of CP
=> CP = 1200
9.(c)
Loss % = ((common gain or loss)/10)^2 %
= (20/10)^2 % = 4%
10.(a)
CP of A = 1818/0.9 = 2020
CP of B = 1818/1.01 = 1800
CP of A/CP of B = 2020/1800 = 101/90
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