A person purchases $90$ clocks and sells $40$ clocks at a gain of $10\%$ and $50$ clocks at a gain of $20\%$. If he sold all of them at a uniform profit of $15\%$, then he would have got Rs. $40$ less. The cost price of each clock is

Let the cost price of each clock be x, making the total cost price 90x. The mixed selling price is calculated as (40 times 1.10x) plus (50 times 1.20x), which equals 44x plus 60x, resulting in 104x. If sold at a uniform 15% profit, the selling price would be 90 times 1.15x, which equals 103.5x. The difference is 104x minus 103.5x, so 0.5x equals 40, meaning each clock costs Rs. 80.

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