Multiple choice

A merchant buys $40$ bicycles and marks them at $25$% above the cost price. He allows a discount on the marked price at $10$% for cash sales and at 5% for credit sales. If three fourth of the stock is sold for cash and the rest for credit and if the total profit is Rs $2025$, what is the cost price of one bicycle?

  1. Rs 350

  2. Rs 720

  3. Rs 360

  4. Rs 460
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let CP = x. MP = 1.25x. Cash sales (3/4 of 40 = 30) at 10% discount: SP = 30 * (1.25x * 0.9) = 33.75x. Credit sales (10) at 5% discount: SP = 10 * (1.25x * 0.95) = 11.875x. Total SP = 45.625x. Total CP = 40x. Profit = 5.625x = 2025. x = 2025 / 5.625 = 360.

AI explanation

Let the cost price of one bicycle be C. The marked price is 1.25C. The selling price for cash is 1.25C multiplied by 0.9, equaling 1.125C, and the selling price for credit is 1.25C multiplied by 0.95, equaling 1.1875C. The average selling price per bicycle is the sum of three quarters of 1.125C and one quarter of 1.1875C, resulting in an average profit of 1.109375C per bicycle. Since the average profit per bicycle is 1.109375C minus C, which equals 0.109375C, and the total profit for 40 bicycles is 2025, we have 40 multiplied by 0.109375C equals 2025. Solving this gives 4.375C equals 2025, making the cost price of one bicycle 360 rupees.

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