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Question
In a mixture of 45 litres, the ratio of milk to water is 13 : 2. How much water must be added to this mixture to make the ratio of milk to water as 3 : 1 ?
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Solution
Mixture of milk and water = 45 litres
Ratio of milk and water =13 : 2
Sum of ratio = 13 + 2 = 15
∴ Quantity of milk = `(45 xx 13)/(15)` = 39 litres
and quantity of water = `45 xx (2)/(15)` = 6 litres
Let x litre of water be added, then water = (6 + x) litres
Now nrew ratio = 3 : 1
∴ 39 : (6 + x) = 3 : 1
`(39)/(6 + x) - (3)/(1)`
⇒ 39 = 18 + 3x
⇒ 3x = 39 – 18 = 21
∴ x = `(21)/(3)` = 7 litres
∴ 7 litres of water is to be added.
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