An individual buys 90 clocks and sells 40 of them with a 10% profit and the remaining 50 with a 20% profit. If all 90 clocks were sold at a uniform profit rate of 15%, he would have earned Rs. 40 less. What is the cost price of each clock?

Explanation

Let the cost price of one clock be Rs. x. The total cost price for 90 clocks is Rs. 90x. The actual total selling price is (40 clocks × 110% of x) + (50 clocks × 120% of x) = 44x + 60x = 104x. If all clocks were sold at 15% profit, total selling price would be 115% of 90x = 103.5x. The difference between actual and uniform selling price is Rs. 40, so: 104x - 103.5x = 40 ⇒ 0.5x = 40 ⇒ x = 80. Therefore, the cost price per clock is Rs. 80.