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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

6. A person, by selling an article at three-fourths of the list price incurs a loss of 20%. Find the profit percentage if he sells at the list price?
 
  • A. 25 %
  • B. 6.66 %
  • C. 5.45 %
  • D. 30 %
Ans: B.
Sol.
0.75 MP = 0.8 CP (since 20% loss) So, MP = 1.0666CP ⇒ 6.66% gain.
 
7. 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
 
8. Mayank Bothra purchased 20 dozens of toys at the rate of 375 Rs per dozen .He sold each one of them at the rate of Rs 33.What was his percentage profit?
 
  • A. 5.6 %
  • B. 6.5 %
  • C. 7.5 %
  • D. 7.6 %
Ans: A.
Sol.
Cost = 375 * 20 = 7500
sale price 33 * 20 * 12
= 7920 profit = 420 profit in % = 420/7500 * 100 =5.6 %
 
9. A person earns 15% on investment but loses 10% on another investment. If the ratio of the two investments be 3:5, what is the gain or loss on the two investments taken together?
 
  • A. 0.63 %
  • B. 0.64 %
  • C. 0.65 %
  • D. 0.66 %
Ans: A.
Sol.
Suppose he invested 300 & 500 respectively profit : 15% of 300 = 45 loss =
500 *10 = 50 net loss = - 5 5/800 *100 = 0.63 %
 
10. A person, by selling an article at three-fourths of the list price incurs a loss of 20%. Find the profit percentage if he sells at the list price?
 
  • A. 18 %
  • B. 25 %
  • C. 6.66 %
  • D. 111/9 %
Ans: C.
Sol.
0.75 MP = 0.8 CP (since 20% loss) So, MP = 1.0666CP ⇒ 6.66% gain.