The C.P. of two shirts taken together is ₹910. If by selling one at a profit of 16% and the other at a loss of 12%, there is no loss or gain in the whole transaction, then the C.P. of the two shirts are respectively:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 390, 520
There is no gain or loss on the whole, so the profit on the first shirt equals the loss on the second.
Assuming the C.P. of the first shirt to be ₹x:
C.P. of the second shirt \(=910-x\)
\(0.16x=0.12(910-x)\)
\(0.28x=109.2\)
\(x=390\), and the second shirt costs \(910-390=520\)
Shortcut:
The costs are in the inverse ratio of the percentages: \(12:16=3:4\), so the costs are \(\displaystyle\frac{3}{7}\times910=390\) and \(\displaystyle\frac{4}{7}\times910=520\).