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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

11. One-fifth of the cost price, one-seventh of the marked price and one-sixth of the selling price are all equal. What is the gain or loss to the trader?
 
  • A. 120 %
  • B. 140 %
  • C. 162/3 %
  • D. 20 %
Ans: D.
Sol.
CP/5 = SP/6 ⇒ SP/CP = 1.2 ⇒ 20% gain.
 
12. If an article is sold at 5% gain instead of 5% loss,the seller gets Rs 6.72 more. The C.P of the article is?
 
  • A. 132.82
  • B. 138.55
  • C. 148.81
  • D. 150.45
Ans: C.
Sol.
100 * 10/6.72 = 148.81 answer
 
13. Peter bought an item at 20% discount on its original price. He sold it with 40% increase on the price he bought it. The sale price is by what percent more than the original price?
 
  • A. 7.2
  • B. 7.5
  • C. 10
  • D. 12
Ans: D.
Sol.
Let the original price be Rs. 100. Then, C.P. = Rs. 80.
S.P. = 140% of Rs. 80 = Rs. [112-100%] = 12%.
 
14. A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been percentage of profit earned of no discount was offered?
 
  • A. 20
  • B. 30
  • C. 35
  • D. 15
Ans: B.
Sol.
Let C.P. be Rs. 100. Then, S.P. = Rs. 123.50.
Let marked price be Rs. x. Then,
95/100x = 123.50 ⇒ x = Rs. [12350/95] = Rs. 130.
Now, S.P. = Rs. 130, C.P. = Rs. 100.
∴ Profit% = 30%.
 
15. Even after reducing the marked price of a transistor by Rs. 32, a shopkeeper makes a profit of 15%. If the cost price be Rs.320, what percentage of profit would he have made if he had sold the transistor at the marked price?
 
  • A. 18 %
  • B. 20 %
  • C. 25 %
  • D. 30 %
Ans: C.
Sol.
C.P. = Rs. 320, Profit = 15%
S.P. Rs. [115/100 * 320] = Rs. 368. Marked price = Rs. (368 + 32) = Rs. 400.
∴ Required profit% = [80/320 * 100] % = 25%.