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A person buys two watches for Rs. 1000 each. He sells one at 10% profit and the other at 10% loss. What is the overall profit or loss?
No profit, no loss
1% loss
1% profit
2% loss
No profit, no loss
When Cost Prices (CP) of two items are equal and one is sold at x% profit and the other at x% loss, the profit percentage always cancels out the loss percentage, resulting in no overall profit or loss.
Cost price of each watch = Rs. 1000, Profit on first watch = 10%, Loss on second watch = 10%.
CPtotalтАЛ=CP1тАЛ+CP2тАЛ, SPtotalтАЛ=SP1тАЛ+SP2тАЛ
When Cost Prices (CP) of two items are equal and one is sold at x% profit and the other at x% loss, the profit percentage always cancels out the loss percentage, resulting in no overall profit or loss.
Students often use the formula 100x2тАЛ loss, which is only applicable when the Selling Price (SP) of both items is the same, not when the Cost Price (CP) is the same.
Calculate Cost Price of both watches
Since both watches cost Rs. 1000 each, the total cost price is:
1000+1000=2000
Calculate Selling Price of the first watch
The first watch is sold at 10% profit:
SP1тАЛ=1000├Ч(1+0.10)=1100
Calculate Selling Price of the second watch
The second watch is sold at 10% loss:
SP2тАЛ=1000├Ч(1тИТ0.10)=900
Calculate total Selling Price and Result
Sum of selling prices is 1100+900=2000. Comparing total SP and total CP (2000тИТ2000=0):
SPtotalтАЛ=1100+900=2000
A is correct because the total cost price (Rs. 2000) is equal to the total selling price (Rs. 2000), resulting in no overall profit or loss.
This concept is a classic trap in Quantitative Aptitude; always identify whether the question specifies that CP is equal or SP is equal before applying any shortcut.
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