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By selling 8 oranges for ₹40, a man loses 20%. How many should he sell for ₹30 to gain 20% in the transaction?
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Calculate the price per orange at a 20% loss (₹40/8 = ₹5). Since 80% of CP = ₹5, 120% of CP = (5/80)*120 = ₹7.5. For ₹30, the number of oranges = 30 / 7.5 = 4.
Selling 8 oranges for ₹40 results in a 20% loss. Selling target is to gain 20% on the transaction.
Cost Price=1−Loss%SellingPrice=1+Gain%SellingPrice
Calculate the price per orange at a 20% loss (₹40/8 = ₹5). Since 80% of CP = ₹5, 120% of CP = (5/80)*120 = ₹7.5. For ₹30, the number of oranges = 30 / 7.5 = 4.
Confusing the loss/gain percentage bases (calculating 20% of the price instead of relating it to Cost Price).
Calculate Cost Price per orange
If selling 8 oranges for ₹40 gives a 20% loss, the CP of 8 oranges is 40 / 0.8 = ₹50. Thus, one orange costs ₹50 / 8 = ₹6.25.
CP=0.840=50
Calculate Target Selling Price
To gain 20%, the SP of one orange must be 120% of its CP, which is 1.2 * 6.25 = ₹7.5.
SPtarget=6.25×1.2=7.5
Find quantity for ₹30
To find how many oranges can be sold for ₹30 at the target price, divide 30 by 7.5.
Quantity=7.530=4
A is correct because the target selling price per orange is ₹7.5, meaning 4 oranges can be sold for ₹30.
This is a standard unitary method problem often found in Ratios and Proportions. Always convert everything to the 'Price per unit' to simplify complex multi-quantity transactions.
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