A person sold his watch for ₹ 75 and got a percentage

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A person sold his watch for ₹ 75 and got a percentage profit equal to the cost price. The cost price of the watch is.

1. ₹ 40
2. ₹ 45
3. ₹ 50
4. ₹ 55

Correct Option: C

Let CP of the watch be ₹ N.
Then , According to the question,
[(75 - N)/ N] x 100 = N
⇒ (75 - N) x 100 = N²
⇒ N² + 100N - 7500 = 0
⇒ N² + 150N - 50N - 7500 = 0
⇒ N(N + 150) - 50 (N + 150) = 0
⇒ (N + 150) (N - 50) = 0
⇒ N = ₹ 50