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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Important Questions from Mixture Problems
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A vessel contains 20 litres containing milk and water in the ratio 3 : 2. Ten litres of this milk is removed and replaced with equal amount of pure milk. If this process is repeated once again, find the final ratio of milk and water.
From a container of 50 liters pure milk, 10 liters is taken out and replaced by 10 liters of water. If this process is repeated thrice, what is the ratio of water and milk finally?
Consider the following statements about a mixture and determine which of the statements is/are correct.
1. A mixture has a variable composition.
2. In compounds, the composition of each new substance is always fixed.
3. A mixture shows the properties of the constituent substances.
