Math CentralQuandaries & Queries


Question from Mahesh, a parent:

A man purchases one shirt and one T-Shirt for Rs. 6000. He sells the shirt at a profit of 20% and T-Shirt at a loss of 10%, as a result he gains 2% on whole transaction. what is the cost price of the T-Shirt ?


Suppose that the price of the shirt is Rs. $S$ and the price of the T-shirt is Rs. $T$ then you know that

\[S + T = 6000.\]

He sells the shirt for a 20% profit so he sells it for Rs.

\[S + \frac{20}{100} \times S = 1.20 \times S.\]

He sells the T-shirt for a loss of 10% so he sells it for Rs.

\[T - 0.10 \times T = 0.90 \times T.\]

The sum of these transactions results is a 2% gain on the Rs. 6000 he paid. This gives you a second equation for $S$ and $T.$ Solve for $T.$


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