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The Cost Price of 100 Mangoes is equal to the selling price of 80 Mangoes. What is the Profit Pecentage?

A. 16% B. 20% C. 24% D. 25% UPSC CDS 1 2021 Elementary Matematics Solution: It is given that CP of 100 Mangoes = SP of 80 Mangoes. Let CP and SP be Cost Price and Selling Price of 1 Mango. We can write that, 100CP = 80SP SP = 100CP/80 SP = 5CP/4 We know that Profit % = ((SP - CP)/CP) * 100 Profit % = ((5CP/4 - CP)/CP) * 100 Profit % = (1/4) * 100 Profit % = 25 % Hence, (d) is the correct answer.
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A trader bought two articles for Rs. 490. He sold one at a loss of 20% and the other at a profit of 16%. If the selling price of both the articles is same, then the cost price (in Rs.) of the article sold at 20% loss will be:

A. 300 B. 280 C. 310 D. 290 SSC CGL 2022 13 August 2021 Shift 1 Solution: Let the articles be A1 and A2 sold at 20% loss and 16% profit respectively. Let the Cost Price (CP) of the A1 for the trader be = x Then the Cost Price (CP) of the A2 for the trader will be = 490 - x It is given that the Selling Price (SP) of A1 and A2 are the same. Let the Selling Price be = y It is given that, On sale of A1, Loss % = 20% On sale of A2, Profit % = 16% We know that, Loss % = ((CP - SP)/CP) * 100 .......(1) Profit % = ((SP - CP)/CP) * 100 ........(2) Putting values in eq. 1 for A1 and in eq. 2 for A2 20 = ((x - y)/x) * 100 .......(3) 16 = ((y - (490 - x))/(490 - x)) * 100 ....(4) From eq. 3, we get 20/100 = 1 - y/x y/x = 1 - 20/100 y/x = 80/100 y = 4x/5 ....(6) Substitute eq. (5) in eq. (4) 16 = ((4x/5 - (490 - x))/(490 - x)) * 100 16/100 = (4x/5)/(490 - x) - 1 4x/(5(490 - x)) = 16/100 + 1 4x/(5(490 - x)) = 116/100 4x/(5(490 - x)) = 29/25 100x = 29 * 5 * (490 - x) 100x = 71050 - 145x 245x...
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