Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150 . Then the number of apples purchased by Aruna is _________.
Explanation:
Let Aruna purchase x apples at 20 each and y mangoes at 25 each. Total cost = 20x + 25y
Case 1: Total selling price of apples = x × 20 × 1.1 = 22x Total selling price of mangoes = y × 25 × 0.8 = 20y Since Aruna had no profit or loss, total cost price = total selling price ∴ 20x + 25y = 22x + 20y ⇒ 5y = 2x ⇒ x : y = 5 : 2 ∴ Let x = 5q and y = 2q ...(1)
Case 2: Total selling price of apples = x × 20 × 0.8 = 16x Total selling price of mangoes = y × 25 × 1.1 = 27.5y Now Aruna incurred a loss of Rs. 150 ∴ 20x + 25y - 150 = 16x + 27.5y ⇒ 4x - 150 = 2.5y ⇒ 20q - 150 = 5q ⇒ q = 10
∴ Number of apples bought by Aruna = x = 5q = 50.
Hence, 50.
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