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PROFIT AND LOSS PROBLEMS

Aptitude

PROFIT AND LOSS -> IMPORTANT FACTS AND FORMULAE

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 purchased, is called its cost price, abbreviated as C.P.
Profit or Gain : The price at which an article is purchased, is called its cost price, abbreviated as C.P.
Loss : If S.Pis less than C.P., the seller is said to have incurred a loss.
1. Gain = (S.P.) - (C.P.)
2. Loss or gain is always reckoned on C.P.
3. gain% = [Gain*100/C.P.]
4. Loss = (C.P.) - (S.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 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.

PROFIT AND LOSS -> SOLVED EXAMPLES

1. If the cost price is 96% of the selling price, then what is the profit percent?
  Sol. Let S.P. = Rs.100. Then, C.P. = Rs. 96; Profit = Rs.4.
∴ Profit% = [4/96 * 100]% = 25/6 % = 4.17%.
2. A person incurs 5% loss by selling a watch for Rs.1140. At what price should the watch be sold to earn 5% profit?
  Sol. S.P. = Rs. 27.50, Profit = 10%.
So, C.P. = Rs.[100/110*27.50] = Rs. 25. When S.P. = Rs. 25.75, profit = Rs. (25.75-25) = Re. 0.75.
∴ Profit% = [0.75/25*100]% = 3%.
3. A person incurs 5% loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit?
  Sol.Let the new S.P. be Rs. x. then,
(100 - loss%) : (1st S.P.) = (100 + gain%) : (2nd S.P.)
⇒ [100-5/1140] = [100+5/x] ⇒ x = [105*1140/95] = 1260.
4. Find S.P when C.P=Rs 56.25 and Gain=20%
  Sol.56.25 * 1.2 = 67.5.
4. If a radio is purchased for Rs 490 and sold for Rs 465.50 Find the loss%?
  Sol.Loss = 490 – 465.5 = 24.5 loss in % = 24.5/ 490 *100 = 5%.

PROFIT AND LOSS -> EXERCISE

16. A shopkeeper sold sarees at Rs. 266 each after giving 5% discout on labelled price. Had he not given the discount, he would have earned a profit of 12% on the cost price. What was the cost price of each saree?
 
  • A. 240
  • B. 250
  • C. 260
  • D. 270
Ans: B.
Sol.
S.P. of 1 saree = Rs.266. Let the labelled price of each saree be Rs. x.
Then, 95/100x = 266 ⇒ x = Rs. [266*100]/95 = Rs. 280.
New, S.P. = Rs. 280, Profit = 12%.
∴ C.P. of 1 saree = Rs. [100/112 * 280] = Rs. 250.
 
17. A shopkeeper sells a badminton racket, whose marked price is Rs. 30, at a discount of 15% and gives a shuttle cock costing Rs. 1.50 free with each racket. Even then he makes a profit of 20%. His cost price per racket is :
 
  • A. 23.50
  • B. 22.50
  • C. 21.00
  • D. 20.00
Ans: D.
Sol.
Marked price = Rs. 30. S.P. = Rs.[(85/100 * 30) - 1.50] = Rs. (25.50 - 1.50) = Rs. 24.
Let C.P. be Rs. x Then, 120% of x = 24 ⇒ x (24 * 100 / 120) = Rs. 20.
 
18. James bought a suitcase with 15% discount on the labelled price. He sold the suitcase for Rs. 2880 with 20% profit on the labelled price. At what price did he buy the suitcase?
 
  • A. 2000
  • B. 2040
  • C. 2140
  • D. 2280
Ans: B.
Sol.
Let the labelled price be Rs. x. Then, 120% of x
= 2880 ⇒ x = [2880 * 100 / 120] = 2400.
∴ C.P. = 85% of Rs. 2400 = Rs. [85 / 100 * 2400] = Rs. 2040.
 
19. The labelled price of a cupboard is Rs. 6500. The shopkeeper sold it by giving 5% discount on the labelled price and earned a profit of 15%. What approximately is the cost price of the cupboard?
 
  • A. 5350
  • B. 5450
  • C. 5500
  • D. 5700
Ans: A.
Sol.
S.P. = 95% of Rs. 6500 = Rs. [95 / 100 * 6500] = Rs. 6175.
Profit = 15%.
∴ C.P. = Rs. [110 / 115 * 6175] = Rs. 5369.56 = Rs. 5350.
 
20. A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is :
 
  • A. 16 %
  • B. 17 %
  • C. 19 %
  • D. 20 %
Ans: D.
Sol.
Let C.P. = Rs. 100. Then, Marked Price = Rs. 135, S.P. = Rs. 108.
∴ Discount % = [27 / 135 * 100] % = 20%.