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A trader lost 10% by selling a shirt for ₹850. He will gain x%' by selling it for ₹1360, the value of x is:
44
54
59
34
44
Calculate CP first: Since 90% of CP = 850, 100% of CP = 850 / 0.9 = 944.44 (Approx). Actually, use ratio: 90% = 850, so 1360 = (1360/850) * 90% of CP = 1.6 * 90% = 144%. Thus, gain is 144% - 100% = 44%.
Selling price SP1 = ₹850, loss percentage = 10%. Selling price SP2 = ₹1360.
CP=1−100Loss%SP1,x%=(CPSP2−CP)×100
Calculate CP first: Since 90% of CP = 850, 100% of CP = 850 / 0.9 = 944.44 (Approx). Actually, use ratio: 90% = 850, so 1360 = (1360/850) * 90% of CP = 1.6 * 90% = 144%. Thus, gain is 144% - 100% = 44%.
Many students calculate profit percentage on the selling price instead of the cost price or misinterpret the 10% loss as a direct deduction from the second selling price.
Calculate Cost Price (CP)
Given that a 10% loss corresponds to ₹850, we represent CP as 100%. Therefore, 90% of CP = 850.
CP=0.90850=944.44
Calculate Percentage of CP for the new SP
To find the new percentage value relative to CP when selling at ₹1360, we find the ratio of SP to CP.
Percentage=850/0.91360×100=8501360×0.9×100=1.6×90=144%
Determine Profit x%
Since the SP represents 144% of the CP, the gain percentage is 144% - 100%.
x=144−100=44
A is correct because selling the shirt for ₹1360 corresponds to 144% of the cost price, resulting in a gain of 44%.
This concept of base-value scaling (90% = SP1, x% = SP2) is frequently used in interest calculations and depreciation problems in Quantitative Aptitude.
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