In what ratio, sugar costing Rs. 60 per kg be mixed with sugar costing Rs. 42 per kg such that by selling the mixture at Rs. 56 per kg there is a gain of 12%?
4 : 5
Step 1 — Find the mixture's cost price. SP = Rs. 56 at 12% gain, so
\[CP=\frac{56}{1.12}=50\text{ Rs/kg}\]
Step 2 — Apply alligation with costs 60 and 42 about mean 50:
\[\frac{\text{Qty at 60}}{\text{Qty at 42}}=\frac{50-42}{60-50}=\frac{8}{10}=\frac{4}{5}\]
Therefore the required ratio is 4 : 5.
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