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A shopkeeper buys 40 bicycles and marks them at 25% above the cost price. He allows a discount of 10% on the marked price for cash sales, and 5% for credit sales. If three-fourth of the stock is sold for cash and the rest for credit, and if the total profit be $ 20250, what is the cost price of a bicycle ?
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- $ 4000
- $ 3500
- $ 3200
- $ 3600
Correct Option: D
Given that , Number of bicycles = 40
Let C.P. of one bicycle be y
| ∴ Marked price of each bicycle = | y = 1.25y | 100 |
Discount for cash sale = 10%
Discount for credit sale = 5%
| ∴ S.P. for cash sale = 1.25 y × | 100 |
S.P. for cash sale = (1.25 y × 0.9) = 1.125 y
| S.P. for credit sale = 1.25 y × | 100 |
S.P. for credit sale = (1.25 y × 0.95) = 1.1875 y
Number of bicycles sold for cash = 30
Number of bicycles sold on credit = 10
∴ Total S.P. = [1.125 y × 30 + 1.1875y × 10] = 45.625 y
∴ Profit = (45.625 – 40) y = 5.625 y
But actual profit = $ 20250
∴ 5.625 y = 20250
| ⇒ y = | = $ 3600 | 5.625 |
Hence, C.P. of a bicycle = $ 3600
