In a 40-litre mixture of milk and water, the ratio of milk to water is 3:1. How much water (in litres) should be added to make this ratio 2:3?

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Accepted Answer

The total quantity of the mixture is 40 litres. Initially, the ratio of milk to water is 3:1.

**Step 1:** Calculate the quantity of milk and water in the mixture.  
Milk = $$ \frac{3}{4} 	imes 40 = 30 $$ litres.  
Water = $$ 40 - 30 = 10 $$ litres.

**Step 2:** Let $$ x $$ litres of water be added to achieve the new ratio of milk to water as 2:3.  
After adding $$ x $$ litres of water, the quantities become:  
Milk = 30 litres (unchanged),  
Water = $$ 10 + x $$.

**Step 3:** Set up the equation for the new ratio:  
$$
\frac{	ext{Milk}}{	ext{Water}} = \frac{2}{3} \implies \frac{30}{10 + x} = \frac{2}{3}.
$$

Cross-multiply:  
$$
3 	imes 30 = 2(10 + x).
$$

Simplify:  
$$
90 = 20 + 2x.
$$

Solve for $$ x $$:  
$$
x = \frac{70}{2} = 35.
$$

Thus, **35 litres of water** should be added to achieve the desired ratio.

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