A clock was sold for ₹107.25. If the percentage of gain was numerically equal to the cost price, the cost of the clock was:

₹65

Best way is to go with answer options.

Check, Profit = 65 *65% = 42.25, it means S.P. = 65 + 42.25 = 107.25 (given)

Therefore, 65 is the cost price.

OR

Gain % = CP

⸫  \(\frac{Gain}{CP}\)  × 100 = CP

SP = 107.25

= \(\frac{107.25-CP}{CP}\) × 100 = CP  

10725 – 100 CP = CP²

CP² + 100 CP – 10725 = 0

CP² – 65 CP + 165 CP – 10725 = 0

CP (CP – 65) + 165 (CP – 65) = 0

(CP – 65) (CP + 165) = 0

⸫        CP = 65       (as CP cannot be negative)