IMPORTANT FACTS
Cost Price:
The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
Selling Price:
The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
Profit or Gain:
If S.P. is greater than C.P., the seller is said to have a profit or gain.
Loss:
If S.P. is less than C.P., the seller is said to have incurred a loss.
IMPORTANT FORMULAE
1.
2.
3.
4.
Gain = (S.P.) - (C.P.)
Loss = (C.P.) - (S.P.)
Loss or gain is always reckoned on C.P.
Gain Percentage: (Gain %)
Gain % =
Gain x 100
C.P.
5. Loss Percentage: (Loss %)
Loss % =
Loss x 100
C.P.
6. Selling Price: (S.P.)
SP =
(100 + Gain %)
x C.P
100
7. Selling Price: (S.P.)
SP =
(100 - Loss %)
x C.P.
100
8. Cost Price: (C.P.)
C.P. =
100
x S.P.
(100 + Gain %)
9. Cost Price: (C.P.)
C.P. =
100
x S.P.
(100 - Loss %)
10. If an article is sold at a gain of say 35%, then S.P. = 135% of C.P.
11. If an article is sold at a loss of say, 35% then S.P. = 65% of 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 the seller always incurs a loss given by:
Loss % =
Common Loss and Gain % 2
=
10
x 2
.
10
13. If a trader professes to sell his goods at cost price, but uses false weights, then
Error
x 100
(True Value) - (Error)
1. Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the
scooter for Rs. 5800, his gain percent is:
4
5
A. 4 %
B. 5 %
7
11
Gain % =
C.
10%
D.
Ans wer & Explanation
Ans wer: Option B
Explanation:
Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) - (C.P.) = Rs.(5800 - 5500) = Rs. 300.
12%
%.
Gain % =
300
5
x 100
=5 %
5500
11
%
2. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%,
then the value of x is:
A.
15
B.
16
C.
18
D.
25
Ans wer & Explanation
Ans wer: Option B
Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
20 - x
x 100 = 25
x
2000 - 100x = 25x
125x = 2000
x = 16.
3. If selling price is doubled, the profit triples. Find the profit percent.
2
A. 66
B. 100
3
1
3
Ans wer & Explanation
C.
105
Ans wer: Option B
Explanation:
Let C.P. be Rs. x and S.P. be Rs. y.
D.
120
Then, 3(y - x) = (2y - x)
y = 2x.
Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x.
Profit % =
x
x 100
x
% = 100%
4. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling
price remains constant, approximately what percentage of the selling price is the profit?
A.
30%
B.
70%
C.
100%
D.
250%
Ans wer & Explanation
Ans wer: Option B
Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage =
295
1475
x 100
=
% = 70% (approximately).
420
21
%
5. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
A.
B.
C.
D.
Ans wer & Explanation
Ans wer: Option C
Explanation:
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs.
For Rs. 6 , toffees sold = 6.
6
5
5
5
= 5.
6
6. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss
incurred by selling the same article for Rs. 1280. At what price should the article be sold to
make 25% profit?
For Re. 1, toffees sold =
6x
A.
Rs. 2000
B.
Rs. 2200
C.
Rs. 2400
D.
Data inadequate
Ans wer & Explanation
Ans wer: Option A
Explanation:
Let C.P. be Rs. x.
Then,
1920 - x
x - 1280
x 100 =
x 100
x
x
1920 - x = x - 1280
2x = 3200
x = 1600
Required S.P. = 125% of Rs. 1600 = Rs.
125
x 1600 = Rs 2000.
100
7. A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392,
what was his profit?
A.
Rs. 18.20
B.
Rs. 70
C.
Rs. 72
D.
Rs. 88.25
Ans wer & Explanation
Ans wer: Option C
Explanation:
C.P. = Rs.
100
x 392
122.5
= Rs.
1000
x 392
1225
= Rs. 320
Profit = Rs. (392 - 320) = Rs. 72.
8. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the
cycle?
A.
Rs. 1090
B.
Rs. 1160
C.
Rs. 1190
D.
Rs. 1202
Ans wer & Explanation
Ans wer: Option C
Explanation:
S.P. = 85% of Rs. 1400 = Rs.
85
x 1400
100
= Rs. 1190
9. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at
the rate of Rs. 33. What was his percentage profit?
A.
3.5
B.
4.5
C.
5.6
D.
6.5
Ans wer & Explanation
Ans wer: Option C
Explanation:
Cost Price of 1 toy = Rs.
375
= Rs. 31.25
12
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % =
1.75
x 100
31.25
28
% = 5.6%
5
10. Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent
is:
A.
30%
B.
331%
3
C.
35%
D.
44%
Ans wer & Explanation
Ans wer: Option D
Explanation:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.
S.P. of 30 articles = Rs.
5
x 30 = Rs. 25.
6
6
x 30 = Rs. 36.
5
11
x 100
25
% = 44%.
11. On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price
of a ball is:
Gain % =
A.
Rs. 45
B.
Rs. 50
C.
Rs. 55
D.
Rs. 60
Ans wer & Explanation
Ans wer: Option D
Explanation:
(C.P. of 17 balls) - (S.P. of 17 balls) = (C.P. of 5 balls)
C.P. of 12 balls = S.P. of 17 balls = Rs.720.
C.P. of 1 ball = Rs.
720
= Rs. 60.
12
12. When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold
in order to gain 15%?
A.
Rs. 21,000
B.
Rs. 22,500
C.
Rs. 25,300
D.
Rs. 25,800
Ans wer & Explanation
Ans wer: Option C
Explanation:
85 : 18700 = 115 : x
x=
18700 x 115
85
= 25300.
Hence, S.P. = Rs. 25,300.
13. 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The
percentage of profit or loss is:
2
A. 14 % gain
B. 15% gain
7
2
14 % loss
7
Ans wer & Explanation
C.
D.
15 % loss
Ans wer: Option A
Explanation:
350
= Rs. 3.50
100
48
S.P. of 1 orange = Rs.
= Rs. 4
12
0.50
100
2
Gain% =
x 100
=
% = 14 %
3.50
7
7
%
C.P. of 1 orange = Rs.
14. A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a
loss of 4%. His total gain or loss percent is:
15
15
A. 5 % loss
B. 5 % gain
17
17
2
6 % gain
3
Ans wer & Explanation
C.
Ans wer: Option B
Explanation:
D.
None of these
100
x 840 = Rs. 700.
120
100
C.P. of 2nd transistor = Rs.
x 960 = Rs. 1000
96
C.P. of 1st transistor = Rs.
So, total C.P. = Rs. (700 + 1000) = Rs. 1700.
Total S.P. = Rs. (840 + 960) = Rs. 1800.
100
15
x 100
=5 %
1700
% 17
Gain % =
15. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per
kg and sells the mixture at Rs. 30 per kg. His profit percent is:
A.
No profit, no loss
B.
5%
C.
8%
D.
10%
E.
None of these
Ans wer & Explanation
Ans wer: Option B
Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =
80
x 100
1600
% = 5%.
