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Gopal purchased a fan and a stool for a total Rs. 1500. He sold the stool at 40% profit and fan at 40% loss. If the selling price of fan and stool were the same, then what is the total loss percent incurred after selling both fan and stool?

Gopal purchased a fan and a stool for a total Rs. 1500. He sold the stool at 40% profit and fan at 40% loss. If the selling price of fan and stool were the same, then what is the total loss percent incurred after selling both fan and stool? Correct Answer 16%

Let CP of stool and fan be ‘x’ and ‘1500 – x’ respectively.

SP of stool = 140% of x = 1.4x

SP of fan = 60% of (1500 – x) = (900 – 0.6x)

According to the question,

1.4x = 900 – 0.6x

⇒ 2x = 900

⇒ x = 450

Total SP = 2 × 1.4x = 2.8x = Rs. 1260

⇒ Loss amount = 1500 – 1260 = Rs. 240

∴ Loss percent = 240/1500 × 100 = 16% 

Smart trick

If two items are sold at same SP, 1st at x% profit and 2nd at x% loss, then overall loss% will be given by (x2/100)%

∴ Loss percentage = (40 × 40)/100 = 16%

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