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A trader lost 10% by selling a shirt for ₹840. He will gain x%' by selling it for ₹1540, the value of x is:
75
55
80
65
65
Calculate CP = SP1 / 0.9 = 840 / 0.9 = 933.33 (approx) is messy. Use Ratio: 90% = 840. So 1% = 840/90. CP(100%) = 8400/9 = 933.33. Then Profit% = ((1540 - 933.33)/933.33) * 100.
Selling Price 1 (SP1) = ₹840, Loss 1 = 10%, Selling Price 2 (SP2) = ₹1540
CP=1−100LSP1,x=(CPSP2−CP)×100
Calculate CP = SP1 / 0.9 = 840 / 0.9 = 933.33 (approx) is messy. Use Ratio: 90% = 840. So 1% = 840/90. CP(100%) = 8400/9 = 933.33. Then Profit% = ((1540 - 933.33)/933.33) * 100.
Many students calculate loss on the Selling Price (840) instead of the Cost Price (CP), or use 10% gain instead of 10% loss.
Calculate Cost Price (CP)
Since there is a 10% loss, the SP represents 90% of the CP. So, CP = 840 / 0.9.
CP=0.9840=98400=32800≈933.33
Calculate Profit Value
Subtract CP from the second selling price to find the absolute profit.
Profit=1540−32800=34620−2800=31820
Calculate Profit Percentage (x%)
Apply the profit percentage formula: (Profit / CP) * 100.
x=(2800/31820/3)×100=28001820×100=65
D is correct because the calculated value of x is 65, representing the profit percentage.
This concept is foundational for 'Discount and Marked Price' problems where you frequently move between CP, SP, and MP using percentages.
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