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Math Topic - Profit & Loss

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Helpful Notes for students who are preparing for competitive exams.

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    PBI Rules and Formulae PBI INSTITUTE PROFIT & LOSS 1. 2. 3. 4. Cost Price . The price, at which an article is purchased, is called its cost price, abbreviated as cost price. Selling Price . The price, at which an article is sold, is called its selling prices, abbreviated as selling price. Profit or Gain : If S.P. is greater than C.P., the seller is said to have a profit or gain. Loss : If S.P. is less than C.P., the seller is said to have incurred a loss. 1). Gain = (S.P.) - (C.P.) 11). Loss = (C.P.) - (S.P.). Ill). Loss or gain is always calculated on C.P. IV). Gain Percentage: (Gain %) Gain = (Gain x 100 / c.P) V). Loss Percentage: (Loss %) Loss % = (Loss x 100 / C.P ) VI). Selling Price: (S.P.) SP = [(100 + Gain 0/0) / 100 x c.P] Vll). Cost Price: (C.P.) C.P. = / (100 + Gain 0/0) x s.P] VIII). If an article is sold at a loss of say, 35% then S.P. = of C.P. If an article is sold at a gain of say 35%, then S.P. = EXERCISE 135% of C.P. 1. A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle? A. Rs. 1090 C. Rs. 1190 Solution S.P B. Rs. 1160 D. Rs. 1202 = of Rs.1400 Rs. 1190.
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    PBI PBI INSTITUTE 2. When a commodity is sold for Rs.34.80, there is a loss of 2%. What is the cost price of the commodity? A. Rs. 26.10 C. Rs. 43.20 Solution B. D. Rs.43 Rs. 46.40 C.P 3. - Rs.(100 / = Rs.46.40. Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit? A. 3.5 c. 5.6 Solution C.P of 1 toy S.P of 1 toy Therefore, Profit B. 4.5 D. 6.5 - Rs.(375/12) - Rs.31.25 = Rs.33. 4. A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%? A. Rs.11.81 C. Rs.12.25 Solution Hence, S.P per Kg B. Rs.12 D. Rs.12.31 = Rs.11.81 = Rs.11.81 5. A shopkeeper give 12% additional discount on the discounted price, after giving an initial discount of 20% on the labelled price of a radio. If the final sale price of the radio is Rs.704, then what is its labelled price? A. Rs. 844.80 C. Rs. 1000 Solution Let the labelled price be Rs.x. B. Rs. 929.28 D. Rs. 1044.80 of 800/0 of x = 704 /88x80) = 1000. 6. A man sells two flats at the rate of Rs.1.995 lakhs each. On one he gains 5% and on the other, he loses 5%. His gain or loss percent in the whole transaction is A. 0.25% loss C. 2.5% loss Solution Loss % B. 0.25% gain D. 25% loss = (5/ 10) 20/
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    7. PBI = (0.5) 20/0 = 0.25%. = Rs.320 - 15 PBI INSTITUTE Peter purchased a machine for Rs. 80,000 and spent Rs.5000 on repair and Rs. 1000 on transport and sold it with 25% profit. At what price did he sell the machine? Solution C.P Profit= S.P 8. Rs.(80000+5000+ 1000) = Rs.86000 25%. = 12.5% of Rs. 86000 =Rs.107500. A shopkeeper expects a gain of 221/20/0 on his cost price. If in a week, his sale was of Rs.392, what was his profit? A. Rs. 18.20 C. Rs. 72 Solution C.P Therefore, Profit B. Rs. 70 D. Rs. 88.25 9. = Rs.(100/122.50x392) = Rs.(1000/1225x392) = Rs.(392-320) By selling a pen for Rs.15, a man loses one sixteenth of what it costs him. The cost price of the pen is A. Rs. 16 C. Rs. 20 Solution Let the C.P be Rs.x.Then, x-i5=x/16 Therefore, C.P= Rs.16. = Rs.72 x-x/16 — x = 16. B. Rs. 18 D. Rs. 21 10. A shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of kilogram weight. Thus, he makes a profit of 200/0 A. c. Solution Therefore,Profit B. 22% D. None of these = 25%.
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    PBI PBI INSTITUTE 11. Samant bought a microwave oven and paid 10 % less than the original price. He sold it with 30% profit on the price he had paid. What percentage of profit did samant earn on the original price? B. 200/0 D. 32% Solution Let the original price Then, C.P S.P of Rs. 90 Required percentage =Rs.100. = Rs.90. = Rs.117. = (117 - 12. If a man reduces the selling price of a fan from Rs.400 to Rs.380, his loss increases by 2%. The cost price of the fan is A. Rs. 480 C. Rs. 600 Solution Let C.P be Rs.x Then, 2% of x B. Rs. 500 D. Rs. 1000 - 380) = 20 13. A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is A. 200/0 Solution Let C.P Then, marked price S.P Discount % =Rs.100 =Rs.135, =Rs.108. - 200/0 14. Kunal bought a suitcase with 15% discount on the labelled price. He said the suitcase for Rs.2880 with 20% profit on the labelled price. At what price did he buy the suitcase? A. Rs.2040 C. Rs.2604 Solution Let the labelled price be Rs.x. 2880 Therefore B. Rs.2400 D. Rs.2640 Then, 120% of x = = 2400.
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    PBI C.P = of Rs.2400 PBI INSTITUTE - Rs(85/100x2400) =Rs.2040. 15. Solution I gain 70 paise on Rs.70. My gain percent is A. 0.1% c. 70/0 B. D. 10/0 100/0 Gain% 16. A book was sold for Rs.27.50 with a profit of 100/0.1f it were sold for Rs.25.75, then what would have been the percentage of profit or loss? A. 20/0 c. 40/0 Solution S.P Then so, C.P when S.P Profit Profit % D. 50/0 = Rs.27.50 Profit= 100/0 = Rs.(100/110 x 27.50) = Rs.25. = Rs.25.75 - Rs.(25.75 - 25) = Rs.O.75.


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