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1. How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

A. 5

B. 2

C. 3

D. 8

Solution:

Total quantity of mixture

\begin{aligned} = \frac{7}{7 + 3} \times 30 litres \\ = 21 litres \end{aligned}

And quantity of water in the mixture

\begin{aligned} = \frac{3}{7 + 3} \times 30 litres \\ = 9 litres \end{aligned}

Let water to be mixed 'a' litre
Then,

\begin{aligned} \Rightarrow (30 + a) \times \frac{40}{100} = 9 + a \\ \Rightarrow 120 + 4 a = 90 + 10 a \\ \Rightarrow 120 - 90 = 10 a - 4 a \\ \Rightarrow 30 = 6 a \\ \Rightarrow a = 5 \end{aligned}

Hence, 5 litres water mixed in the mixture.

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