Problems on Profit Loss
Q1. A chair is bought for Rs. 450 and sold at Rs. 740. Find the gain percent
(a) 17 | 1 | % |
7 |
(b) 25 | 1 | % |
3 |
(c) 43 | 1 | % |
7 |
(d) 64 | 4 | % |
9 |
Answer:
(d) 64 | 4 | % |
9 |
Here C.P = Rs. 450 and S.P = Rs. 740
∴ Gain = Rs. (740 - 450) = Rs. 290
∴ Gain % = | 290 | X 100% | = 64 | 4 | % |
450 | 9 |
Q2. If a man were to sell his chair for Rs. 620, he would loss 20%. To gain 25%, he should sell it for
(a) 873.77
(b) 968.75
(c) 1010.55
(d) 1123.36
Answer: (b) 968.75
Let the C.P of the chair be Rs. x
S.P = Rs. 620
Loss = 20%
A/Q, x - | 20x | = 620 |
100 |
⇒ x - | x | = 620 |
5 |
⇒ | 4x | = 620 |
5 |
⇒ x = | 620 X 5 | = 775 |
4 |
∴ C.P = Rs. 775
To gain 25%,
C.P = Rs. 775
∴ S.P = Rs. (775 + 775 X (25/100))
= Rs. (775 + 193.75)
=Rs. 968.75
Q3. A man sell his type writer at 5% loss. If he sells it for Rs. 80 more, he gains 5%. The cost price of the typewriter is
(a) 800
(b) 830
(c) 870
(d) 890
Answer: (a) 800
Let the cost price be Rs. x
∴ | 105 | X x - | 95 | X x = 80 |
100 | 100 |
⇒ | 21x | - | 19x | = 80 |
20 | 20 |
⇒ 21x - 19x = 1600
⇒ 2x = 1600
⇒ x = 800
∴ C.P = Rs. 800
Q4. Amit sold a bag for Rs. 540, losing 10%. The cost price of the bag is
(a) 400
(b) 550
(c) 600
(d) 850
Answer: (c) 600
Let the cost price be Rs. x
S.P = Rs. 540
Loss % = 10%
Now x - x X | 10 | = 540 |
100 |
⇒ | 10x -x | = 540 |
10 |
⇒ 9x = 5400
⇒ x = 600
∴ C.P = rs. 600
Q5. A bookseller sells a book at a gain of 10%. If he had bought it at 5% less and sold it for Rs. 5 more, he would have gained 18¾ %. The cost price of the book is
(a) 112.35
(b) 120.50
(c) 133.33
(d) 149.80
Answer: (c) 133.33
Let the cost price of the book is Rs. x
∴ S.P = x + x X | 10 | = | 110x | = Rs. | 11x |
100 | 100 | 10 |
New C.P = 95% of x = x X | 95 | = | 19x |
100 | 20 |
New S.P = Rs. ( | 11x | + 5 ) |
10 |
Now S.P - C.P = x X 18 | 3 | % |
4 |
⇒ | 11x | + 5 - | 19x | = x X | 75 |
10 | 20 | 4 X 100 |
⇒ | 22x + 100 - 19x | = | 75x |
20 | 400 |
⇒ 3x + 100 = | 75x | X 20 |
400 |
⇒ 12x + 400 = 15x
⇒ 3x = 400
⇒ x = 133.33
∴ C.P = Rs. 133.33
Q6. Hari bought 1200 eggs at Rs. 4 per dozen. He sold 900 of them at 2 for Rs. 1 and the remaining at 5 for Rs. 2. His gain percent is
(a) 35.3 %
(b) 42.5 %
(c) 49.3 %
(d) 56.8 %
Answer: (b) 42.5 %
C.P = Rs. ( | 1200 | X 4 ) = Rs. 400 |
12 |
S.P = Rs. ( | 900 | + | 2 X 300 | ) = Rs. (450 + 120) = Rs. 570 |
2 | 5 |
∴ Gain = Rs. (570 - 400) = Rs. 170
Gain% = | 170 | X 100 | = 42.5 % |
400 |
Q7. A merchant has 1000 kg of Rice, part of which sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% is
(a) 350 Kg
(b) 420 Kg
(c) 540 Kg
(d) 600 Kg
Answer: (d) 600 Kg
Let the C.P of 1 kg Rice be Rs. x
∴ C.P of 1000 Kg Rice = Rs. 1000x
Let the Rice sold at 8% gain be y Kg
Then the Rice sold at 18% gain = (1000 - y) Kg
∴ ( | 108 | X xy) + [ | 118 | X x (1000 - y)] = | 114 | X 1000x |
100 | 100 | 100 |
⇒ | 27y | + | 59 (1000 - y) | = 1140 |
25 | 50 |
⇒ 54y + 59(1000 - y) = 57000
⇒ 5y = 2000
⇒ y = 400
∴ Required quantity = (1000 - 400)kg = 600 kg
Q8. A radio is sold for Rs. 880 at a profit of 10%. What would have been the gain or loss percent, had it been sold for Rs. 780 ?
(a) 2½ %
(b) 3¼ %
(c) 3½ %
(d) 5¾ %
Answer: (a) 2½ %
Let, the C.P be Rs. x
S.P = Rs. 880
Profit% = 10%
Now, x + x X (10/100) = 880
⇒ x + x/10 = 880
⇒ 11x/10 = 880
⇒ x = (880 X 10)/11 = 800
∴ C.P = Rs. 800
New S.P = Rs. 780
∴ Loss = Rs. (800 - 780) = Rs. 20
∴ Loss % = (20/800) X 100 = 2½ %
Q9. A man sold an article at a loss of 10%. If he sells the article for Rs. 10 more he would have gained 5%. The cost price of the article is
(a) Rs. 30
(b) Rs. 36.50
(c) Rs. 54.76
(d) Rs. 66.66
Answer: (d) Rs. 66.66
Let the C.P be Rs. x
Loss = 10%
∴ S.P = x - (10x/100) = x - (x/10) = Rs. 9x/10
New S.P = Rs. ( | 9x | + 10) = Rs. | 9x + 100 |
10 | 10 |
Now | 9x + 100 | - x = x X | 5 |
10 | 100 |
⇒ | 9x + 100 - 10x | = | x |
10 | 20 |
⇒ -x + 100 = x/2
⇒ x/2 + x = 100
⇒ 3x/2 = 100
⇒ x = 200/3 = 66.66
∴ C.P = Rs. 66.66
Q10. Mangoes are bought at 5 for Rs. 20 and sold at 6 for Rs. 30. His gain percent is
(a) 18%
(b) 21%
(c) 25%
(d) 28%
Answer: (c) 25%
C.P = Rs. 20/5 = Rs. 4 for one mango
S.P = Rs. 30/6 = Rs. 5 for one mango
∴ Gain = Rs (5 - 4) = Rs. 1
Gain% = (1/4) X 100% = 25 %