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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

21. A trader marked the selling price of an article at 10% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed a discount of :
 
  • A. 10 %
  • B. 10.5 %
  • C. 11 %
  • D. 12.5 %
Ans: A.
Sol.
Let C.P. = Rs. 100. Then, Marked Price = Rs. 110, S.P. = Rs. 99.
∴ Discount % = [11/110 * 100] % = 10%
 
22. The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%.
 
  • A. 37.5 %
  • B. 38.5 %
  • C. 42 %
  • D. 27.5 %
Ans: A.
Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 64. S.P = Rs. 88.
∴ Gain % = [24/64 * 100]% = 37.5%.
 
23. By selling an umbrella for Rs. 300, a shopkeeper gains 20%. During a clearance sale, the shopkeeper alows a discount of 10% on the marked price. His gain percent during the sale is :
 
  • A. 6
  • B. 7
  • C. 8
  • D. 9
Ans: C.
Sol.
Marked price = Rs. 300. C.P. = Rs. [100 / 120 * 300] = Rs.250.
Sale price = 90% of Rs. 300 = Rs. 270.
∴ Required gain% = [20 / 250 * 100] % = 8%.
 
24. A trader marked the price of his commodity so as to include a profit of 25%. He allowed discount of 16% on the marked price. His actual profit was :
 
  • A. 4
  • B. 5
  • C. 10
  • D. 12
Ans: B.
Sol.
Let C.P. be Rs. 100. Then, marked price = Rs. 125.
S.P. = 84% of Rs. 125 = Rs. [84 /100 * 125] = Rs. 105.
∴ Profit% = (105 - 100)% = 5%.
 
25. A bag marked at Rs. 80 is sold for Rs. 68. The rate of discount is :
 
  • A. 12 %
  • B. 13 %
  • C. 15 %
  • D. 18 %
Ans: C.
Sol.
Rate of discount = [12/80 * 100] % = 15%.