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1. The ratio of spirit and water in two mixtures of 20 litres and 36 litres is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is ?

A. 25 : 29

B. 9 : 10

C. 27 : 29

D. 27 : 31

Solution:

\begin{aligned} According to the question, \\ Mixture - 1  =  20 litres \\ Mixture - 2  =  36 litres \\ In Mixture - 1 ratio of \\ \frac{Spirit}{Water} = \frac{3}{7} ⟩ 10 units \\ In Mixture - 2 ratio of \\ \frac{Spirit}{Water} = \frac{7}{5} ⟩ 12 units \\ 10 units \to 20 litres \\ 1 unit \to 2 litres \\ 12 units \to 36 litres \\ 1 unit \to 3 litres \\ ∴ In Mixture - 1 ratio of \\ \frac{Spirit}{Water} = \frac{3 \times 2}{7 \times 2} = \frac{6}{14} \\ ∴ In Mixture - 2 ratio of \\ \frac{Spirit}{Water} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \\ Ratio of spirits and water \\ = \frac{6 + 21}{14 + 15} \\ = \frac{27}{29} \\ = 27:29 \end{aligned}

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