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.
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.
मैंने ₹1,200 में दो ड्रेस खरीदीं। मैंने पहली ड्रेस को 9% की हानि पर और दूसरी ड्रेस को 18% के लाभ पर बेच दिया। यदि कुल मिलाकर मुझे न तो हानि हुई और न ही लाभ हुआ, तो पहली ड्रेस का क्रय मूल्य (₹ में) ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
800
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
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