Profit and Loss [लाभ और हानि]–11

Question: A shopkeeper sells two watches for Rs. 308 each. On one he gets 12% profit and on the other 12% loss. His profit or loss in the entire transaction was [Ans. (a) 1& 11/25% loss] 

(a) 1& 11/25% loss (b) 1 & 11/25% gain (c) 3 & 2/25% loss (d) 3 & 2/25% gain (e) None of these

Solution:

Detailed Explanation:

Concept: When two articles are sold at the same price and there is gain on one article, while there is loss on the other, and if the numerical value of profit and loss are the same; then in the whole deal, there will also be loss. Loss percentage is given by x²/100%.

First Method: Here, the selling prices are the same and 12% profit is on one and 12% loss on the other. 

Therefore, loss % = x²/100% = (12)²/100% = 144/100% = 1.44% = 1 & 11/25%

Second Method: When the selling prices are the same, it can be assumed as any number. So, avoiding the given selling price of Rs. 308, we assume a new number as selling price. As profit on one is 12%, so we take (100-12) and there is a loss of 12%, so we take (100-12). Let the selling price of each article is (100+12) × (100-12) = 112×88. Selling price of both the watches is 2×112×88  

SP = 2×112×88 =2× 9856 = 19712

CP of both watches = (112×88) ×100/88 + (112×88) ×100/112

Or, CP = 11200+8800 = 20000

Loss = 288

Loss% = (288/20000) ×100% = 1.44% = Ans.

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