A grocer buys 56 kg of sugar of two kinds, costing Rs. 35 per kg and Rs. 42 per kg, for a total of Rs. 2240. How many kg of the cheaper sugar did he buy?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16 kg
The mean price of the whole purchase decides the ratio of the two kinds by the rule of alligation.
\(\displaystyle \text{Mean price} = \frac{2240}{56} = 40\)
\(\text{Cheaper} : \text{Dearer} = (42 - 40) : (40 - 35) = 2 : 5\)
\(\displaystyle \text{Cheaper sugar} = \frac{2}{7} \times 56 = 16 \text{ kg}\)
Check: \(16 \times 35 + 40 \times 42 = 560 + 1680 = 2240\).
So he bought 16 kg of the cheaper sugar.