Question : A person sold two items each for INR 42,600. On the first item, he made a loss of 25%, while on the second, he gained 20%. Find his overall percentage gain or loss, giving your answer correct to one place of decimal.
Option 1: 7.7% gain
Option 2: 7.7% loss
Option 3: 8.3% loss
Option 4: 8.2% loss
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Correct Answer: 7.7% loss
Solution :
Here the cost price is denoted by CP, the selling price is denoted by SP.
He sold both the items for Rs. 42,600.
On the first item, he made a loss of 25%
CP of the first item $= 42,600\times \frac{100}{(100-25 \%)} = 56800$
On the second item, he gained $20$%
CP of 2nd item $= 42,600\times \frac{100}{(100+20 \%)} = 35500$
Total CP of both items is = Rs. 56,800 + Rs. 35,500 = Rs. 92,300
Total SP of both items is = Rs. 42,600 + Rs. 42,600 = Rs. 85,200
Loss = Rs. 92,300 – Rs.85,200 = Rs. 7,100
Loss % = $\frac{7100}{92300}\times 100 = 7.7$%
Hence, the correct answer is a 7.7% loss.
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