Multiple choice

A man buys two cycles at a total cost of Rs. 900. By selling one cycle for 4/5th of its cost and the other for 5/4th of its cost, he makes a profit of Rs. 90 on the whole transaction. Find the cost prices of both the cycles.

  1. Rs. 300 and Rs. 600, respectively

  2. Rs. 400 and Rs. 500, respectively

  3. Rs. 450 and Rs. 450, respectively

  4. Rs. 700 and Rs. 200, respectively

  5. Rs. 500 and Rs. 100, respectively
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A Correct answer
Explanation

Let CP1 = x, CP2 = 900 - x. Profit = (5/4)x - x + (4/5)(900 - x) - (900 - x) = 90. (1/4)x - (1/5)(900 - x) = 90. (1/4)x - 180 + (1/5)x = 90. (9/20)x = 270. x = 600. CP1 = 600, CP2 = 300.

AI explanation

Let the cost price of the first cycle be x, making the second cycle's cost 900 - x. The selling prices are 0.8x and 1.25(900 - x) respectively, and their sum must equal the total cost plus the profit (900 + 90 = 990). Solving the equation 0.8x + 1125 - 1.25x = 990 results in 0.45x = 135, so x = 300. The cost prices of the two cycles are Rs. 300 and Rs. 600 respectively.

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