Number System - Profit & Loss
Cost Price, (c.p.) = The price, at which an article is purchased, is called its cost price.
Selling price (s.p) = The price, at which an article is sold, is called its selling price.
Profit or Gain = (S.P) - (C.P)
Loss = (C.P) - (S.P)
Gain or Loss is always reckoned on C.P.
Formulae
Gain% = (Gain*100) / C.P
Loss% = (Loss*100) / C.P
S.P = (100+ Gain %) /100 * (C.P)
S.P = (100-Loss %) / 100 * (C.P)
C.P = 100 / (100 + Gain %)* (S.P)
C.P = 100 / (100-Loss %)* (S.P)
Important cases
If an article is sold at a profit of say, 20%, then SP = 120% of CP.
If an article is sold at a loss of say, 20%, then SP = 80% of CP.
When a person sells two similar items, one at a gain of say x% and the other at a loss of say x%. then the seller always incurs a loss given by:
Loss% = (x/10)2 If a seller sells his goods at cost price but uses false weights, then
Gain% = [Error/(True value - Error) * 100]%
Solved Examples
Q 1 - A vendor bought 6 oranges for Re 10 and sold them at 4 for Re 6. Find his loss or gain percent.
Answer - D
Explanation
Suppose, number of oranges bought = LCM of 6 and 4 = 12 ∴CP = Re (10/6 * 12) = Re 20 and SP = Re (6/4 * 12) = Re 18 ∴Loss% = (2/20 * 100)% = 10%
Q 2 - By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.
Answer - A
Explanation
(SP of 33m) - (CP of 33m) = Gain = SP of 11m ∴ SP of 22m = CP of 33m Let CP of each meter be Re 1. Then, CP of 22m = Re 22. Hence SP of 22m = Re 33. ∴ %Gain = 11/22 * 100 = 50%
Q 3 - Pure ghee costs Re 100 per kg. A shopkeeper mixes vegetable oil costing Re 50 per kg and sells the mixture at Re 96 per kg, making a profit of 20%. In what ratio does he mix the pure ghee with the vegetable oil.
Answer - A
Explanation
Mean Cost price = Re (100/120)*96 = Re 80 per kg Apply rule of allegation,there4; Required ratio = 30:20 = 3:2
Q 4 - The CP of 25 articles is equal to SP of 20 articles. Find the loss or gain percent.
Answer - C
Explanation
Let the CP of each article = Re 1. Then CP of 20 articles = Re 20. SP of 20 articles = CP of 25 articles = Re 25. ∴ Gain% = (5/20)*100% = 25%
Q 5 - A shopkeeper bought 80 kg of sugar at Re 13.50/kg and mixed it with 120 kg sugar at Re 16/kg. If he is to make a profit of 16% what rate should he sell the sugar to his customers?
Answer - D
Explanation
CP of 200 kg of mixture = Re (80 * 13.50) + (120 * 16) = Re 3000 SP = 116% of Re 3000 = Re (116/100)*3000 = Re 3480 ∴Rate of SP = Re 3480/200 = Re 17.40/kg
Q 6 - A man bought cookies at 3 for a rupee. How many for a rupee should he sell to make a profit a 50%.
Answer - B
Explanation
CP of 3 cookies = Re 1 SP of 3 cookies = 150% of Re 1 = 3/2 For Re 3/2, the man sells 3 cookies. Hence for Re 1, number of cookies sold = 3*2/3 = 2
Q 7 - Anil buys a calculator for Re 600 and sells it to Vikash at 10% profit. Vikash sells it to Chandan for 5 % profit. Chandan after using it for certain time, sells it to Dinesh at a loss of 20%. For how much Chandan sell the calculator to Dinesh.
Answer - C
Explanation
SP for Chandan = 600 * (110/100) * (105/100) * (80/100) = 600 * 924/1000 = Re 554.40
Q 8 - An article is sold by X to Y at a loss of 20%, Y to Z at a gain of 15%, Z to W at a loss of 5% and W to V at a profit of 10%. If v had to pay Re 500, how much X paid for it?
Answer - A
Explanation
CP for X = 500 * (100/80) * (100/115) * (100/95) * (100/110) = 500 * 10000/9614 = Re 520.07
Q 9 - A vendor when could not find buyers for his vegetable at Re 10/kg, reduced the rate to Re 8.10 per kg but uses a faulty weight of 900 gm in place of 1 kg weight. Find the percent change in the actual price or loss.
Answer - D
Explanation
After the price was reduced, 900 gm now costs Re 8.10. Hence 1000gm will cost (1000/900)*8.10 = Re 9 % change in actual price or loss = [(10 - 9)/10]*100% = 10%
Q 10 - A trader marks the SP of an object at a profit of 20%. Considering the demand o the object, he further increases the price by 10%. Find the final profit %.
Answer - C
Explanation
Let the CP = Re 100 ∴ SP = 100 * (120/100) * (110/100) = Re 132 Final profit = (132 - 100)*100% = 32%
Q 11 - An article when sold for Re 4600 makes a 15% profit. Find the profit or loss % if it was sold for Re 3600.
Answer - C
Explanation
CP = 4600 * (100/115) =Re 4000 Loss% = [(4000-3600)/4000]*100% = 10%
Q 12 - A seller sells a watch at 5% loss. If he had bought it at 20% more and sold it for Re 115 less, he would have incurred a loss of 40%. Find the cost price of the watch.
Answer - A
Explanation
Assume CP = x Selling price at the first case = (95/100)x Selling price at the second case = (60/100)*(120/100)x = (7200/10000)x As per question, (95/100)x - (7200/10000)x = 150 Or, x = Re 500
Q 13 - When a man sold an article for Re 540, he made a loss of 10%. At what price should he sell it, so that he incurs a loss of only 5%.
Answer - D
Explanation
CP = 540*(100/90) = Re 600 New SP = 600*(95/100) = Re 570
Q 14 - Ram sells chocolates at a profit of 20% for Re 60. What will be the percentage loss or gain if he reduces the price to Re 55 due to less demand.
Answer - C
Explanation
CP = 60*(100/120) = Re 50 New SP = Re 55 Gain% = (5/50)*100 =10%
Q 15 - A shopkeeper buys rice for Re 1600. He had to sell 1/4th at a loss of 20%. If he is to make an overall gain of 10%, what percentage of profit he needs to make out of the remaining stock of rice?
Answer - A
Explanation
CP of 1/4th of the stock = 1600/4 = Re 400 SP of 1/4th of the stock = 400*(80/100) =Re 320 In order to make a profit of 10% on total CP, the SP should be: SP = 1600*(110/100) = Re 1760 ∴The SP for the remaining 3/4th of the stock should be Re 1760 - Re 320 = Re 1440. Cost Price of the 3/4th of stock = Re 1600 - Re 400 = Re 1200. ∴%Gain = [(1440-1200)/1200*100}] = (240/1200)*100 = 20%
Q 16 - A 10% hike in the price of wheat forces a person to purchase 2 kg less for Re 110. Find the new and the original price of the wheat.
Answer - B
Explanation
10% of Re 110 = Re 11 Cost of 2 kg of wheat at new price = Re 11 So, cost of 1 kg of wheat at new price = Re 5.50 = Re 11/2 Original Price = (11/2)*(100/110) = Re 5 per kg
Q 17 - 10 kg of rice costs as much as 20 kg of wheat, 25 kg of wheat costs as much as 2kg of tea, 5 kg of tea costs as much as 25kg of sugar. Find the cost of 6 kg of sugar if 14 kg of rice costs Re 32.
Answer - C
Explanation
4 kg of rice costs Re 32 ∴10kg of rice will cost = (32/4)*10 = Re 80 20 kg of wheat costs Re 80. ∴25kg of wheat costs = (80/20)*25 = Re 100 2kg of tea costs Re 100 ∴5 kg of tea costs = (100/2)*5 = Re 250 25kg of sugar costs Re 250. ∴6 kg of sugar costs = (250/25)*6 = Re 60
Q 18 - A fruit seller sells bananas at a profit of 20%. If he increases the selling price of each banana by 25 paisa, he earns a profit of 45%. Find the initial selling price of each banana and also its cost price.
Answer - A
Explanation
Let CP = x paisa. Initial SP = x*(120/100) paisa As per question, 120x/100 + 25 = (145/100)x or, 145x/100 - 120x/100 = 25 or, 25x/100 = 25 or, x = 100 paisa CP = 100 paisa or Re 1. Initial SP = 120 paisa or Re 1.20.
Q 19 - A man sold two plots for Re 8 lakhs each. One on he earns a profit of 16% and the other he loses 16%. How much does he loss or gain in the whole transaction?
Answer - C
Explanation
Applying direct formula, %loss = (16/10)2% = 64/25% = 2.56%
Q 20 - 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?
Answer - B
Explanation
Let CP = Re 100. The, marked price, MP = Re 150 SP = 75% of Re 150 = Re 112.50 ∴ Gain% = 12.50%