If half of the quantity of sugar in a bag was sold at a profit of 20%, a quarter of the quantity of sugar in the bag was sold at a profit of 16%, and the remaining sugar in the bag was sold at a profit of 24%, and the total profit obtained by selling all the sugar in the bag was ₹90, what was the cost price of the entire quantity of sugar in the bag?
Explanation:
Let the total quantity of the sugar in bag = 100 kg while cost price of sugar is Rs. x/kg.
50 kg is sold at 20% profit, hence profit = 50 × 0.2x = 10x 25 kg is sold at 16% profit, hence profit = 25 × 0.16x = 4x 25 kg is sold at 24% profit, hence profit = 25 × 0.24x = 6x
∴ Total profit = 10x + 4x + 6x = 20x
Now, 20x = 90 ⇒ x = 4.5
∴ Total cost price of the bag of sugar = 100x = Rs. 450
Hence, option (a).
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