Question

Given below are two statements : **Statement I :** In order to get a mixture worth ₹ 16.5/kg, a grocer needs to mix two varieties of pulses costing ₹ 15 and ₹ 20 per kg respectively in the ratio 7 : 3. **Statement II :** A merchant has 1000 kg rice, part of which he sells at 8 % profit and the rest at 16 % profit. He gains 14 % on the whole. The quantity of rice sold at 16 % profit is 750 kg. In the light of the above statements, choose the correct answer from the option given below:

Accepted Answer

A. **Statement I:** Weighted average price = $\frac{7 	imes 15 + 3 	imes 20}{7 + 3} = \frac{105 + 60}{10} = \frac{165}{10} = 16.5$. So Statement I is true. **Statement II:** By alligation ratio of quantities at 8% and 16%: $(16 - 14) : (14 - 8) = 2 : 6 = 1 : 3$. Quantity sold at 16% profit = $\frac{3}{4} 	imes 1000 = 750$ kg. So Statement II is true. Hence, Option A is correct.

Mixtures and Alligation Statements

Explanation

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