Ten litres are drawn from a drum full of water and replaced by pure mi...
**Problem Statement:**
Ten liters are drawn from a drum full of water and replaced by pure milk. Ten liters of the resulting solution is then replaced by pure milk. The drum now contains milk and water in the ratio 9:16. What is the capacity of the drum?
**Solution:**
To solve this problem, we can follow the steps below:
1. **Analyze the first replacement:**
- Let's assume the initial capacity of the drum is 'x' liters.
- After drawing 10 liters of water, the remaining water in the drum is (x - 10) liters.
- Since 10 liters of pure milk is added, the milk content in the drum is now 10 liters.
- So, the ratio of milk to water after the first replacement is 10:(x - 10).
- Simplifying this ratio, we get (1/1):(x/10 - 1).
2. **Analyze the second replacement:**
- After the second replacement, the ratio of milk to water becomes 9:16.
- So, the remaining milk in the drum is (9/25) times the total content.
- The remaining water in the drum is (16/25) times the total content.
- Therefore, we have the equation: (9/25)x = (16/25)(x - 10).
3. **Solve the equation:**
- Multiply both sides of the equation by 25 to eliminate the fractions: 9x = 16(x - 10).
- Expand the equation: 9x = 16x - 160.
- Simplify the equation: 160 = 7x.
- Divide both sides by 7: x = 160/7.
4. **Calculate the capacity of the drum:**
- The capacity of the drum is given by 'x', which we calculated as 160/7 liters.
- So, the capacity of the drum is approximately 22.86 liters.
Therefore, the capacity of the drum is approximately 22.86 liters.