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PROFIT AND LOSS PROBLEMS

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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

1. An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the marked price. What is his actual profit on the sales?
 
  • A. 12.50 %
  • B. 13.50 %
  • C. 14 %
  • D. 14.50 %
Ans: A.
Sol.
Let C.P. = Rs. 100. Then, marked price = Rs. 150.
S.P. = 75% of Rs. 150 = Rs. 112.50.
∴ Gain% = 12.50%.
 
2. A retailer buys 40 pens at the marked price of 35 pens from a wholesaler. If he sells these pens giving a discount of 1%, what is the profit percent?
 
  • A. 12 %
  • B. 10 %
  • C. 15 %
  • D. 16 %
Ans: B.
Sol.
Let the marked price of each pen be Re. 1.
Then, C.P. of 40 pens = Rs. 36. S.P. of 40 pens = 99% of Rs. 40 = Rs. 39.60.
∴ Profit% = [3.60/36 * 100]% = 10%.
 
3. John bought 15 apples for Rs.10 and sold them at the rate of 12 apples for Rs.12. What is the percentage of profit made by him?
 
  • A. 50 %
  • B. 60 %
  • C. 65 %
  • D. 100 %
Ans: A.
Sol.
He got profit ⇒ profit % = 15/10 * 12/12 = 1.5 ⇒ 50%.
 
4. 30% loss on cost price in what percent loss on selling price?
 
  • A. 28.44 %
  • B. 38 %
  • C. 40.35 %
  • D. 42.85 %
Ans: D.
Sol.
Loss = 30% on CP i.e., 0.3CP ⇒ SP = 0.7CP Loss % on
SP = loss/SP * 100 = 0.3CP/0.7CP * 100 = 42.85%.
 
5. David purchased a house for Rs.75000 and a site for Rs.15000 respectively, if he sold the house for Rs.83000 and the site for Rs.10000, then find the resultant percentage of gain?
 
  • A. 30 %
  • B. 330/3 %
  • C. 31/3 %
  • D. 3.33 %
Ans: D.
Sol.
Total CP = 90000 & total SP = 93000 ⇒ gain = SP/CP = 93000/90000 = 1.0333 = 3.33%.