I bought two dresses for ₹1,200. I sold the first one at a loss of 9% and the second at a gain of 18%. If, on the whole I made neither a loss nor a gain, find the cost price (in ₹) of the first dress.

Solution:

Let cost price of first dress = x
Then cost price of second dress = 1200 − x

First dress (9% loss):
SP = $ 0.91x $

Second dress (18% gain):
SP = $ 1.18(1200 - x) $

Since there is no profit, no loss overall:
Total SP = Total CP

$ 0.91x + 1.18(1200 - x) = 1200 $

Solve:

$ 0.91x + 1416 - 1.18x = 1200 $

$ -0.27x + 1416 = 1200 $

$ -0.27x = -216 $

$ x = 800 $

Final Answer: ₹800