A merchant has 1000 kg of sugar, part of which he sells at 8% proflt and the rest at 18% profit. He gains 14% on the whole. The quantity (in kg.) sold at 18% profit is :
A merchant has 1000 kg of sugar, part of which he sells at 8% proflt and the rest at 18% profit. He gains 14% on the whole. The quantity (in kg.) sold at 18% profit is :
A560
B600
C400
D640
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Correct answer is: 600
Explanation:Given:
\(\text{Quantity of sugar = 1000 kg}\)
Calculation:
\(\text{Let cost price of 1kg of sugar be Rs.100.}\)
\(\text{Selling price of 1kg sugar sold at 8% profit = 100} \times \frac{108}{100}\text{= Rs.108}\)
\(\text{Selling price of 1kg sugar sold at 18% profit =} 100 \times \frac{118}{100} \text{= Rs.118}\)
\(\text{Average selling price of 1kg sugar =} 100 \times \frac{114}{100} \text{= Rs.114}\)
Using rule of alligation,
\(\text{Ratio of sugar sold at 8% and 18% profit =} (118 - 114) : (114 - 108) = 4 : 6 = 2 : 3\)
\(\therefore \text{Quantity sold at 18% profit}= \frac{3}{5} \times 1000 = \text{ 600 kg}\)
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