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A trader lost 10% by selling a shirt for ₹850. He will gain x%' by selling it for ₹1530, the value of x is:
77
52
72
62
62
Use the ratio of selling prices: SP2SP1=1+Gain1−Loss. Given 1530850=1+x%0.9. Simplify 15385=95, so 95=1+x%0.9. Thus 1+x%=0.9×59=1.62. So x=62.
Selling Price 1 (SP1) = ₹850, Loss = 10%, Selling Price 2 (SP2) = ₹1530.
CP=1−Loss%SP1,Gain%=CPSP2−CP×100
Use the ratio of selling prices: SP2SP1=1+Gain1−Loss. Given 1530850=1+x%0.9. Simplify 15385=95, so 95=1+x%0.9. Thus 1+x%=0.9×59=1.62. So x=62.
Students often calculate 10% of ₹850 instead of finding the Cost Price using the loss percentage formula, leading to an incorrect base for the gain calculation.
Calculate Cost Price (CP)
Since there is a 10% loss, the shirt was sold at 90% of its CP. So, 0.9×CP=850.
CP=0.9850=98500
Calculate Gain Percent
The gain percentage is calculated as CPSP2−CP×100. Substituting the values: 8500/91530−(8500/9)×100.
Gain%=850013770−8500×100=85005270×100=62%
D is correct because the calculated gain percentage is 62%.
This concept of 'Ratio of SP' is highly useful in Profit & Loss questions to avoid calculating large fractional Cost Prices, saving significant time in exams.
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