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 Answer: Option CShow Answer
Solution(By Apex Team)
$\begin{array}{l}\text{According to the question,}\\
\text{Mixture -1}=20\ \text{litres}\\
\text{Mixture -2}=36\ \text{litres}\\
\text{In Mixture -1 ratio of}\\
\left.\Large\frac{\text { Spirit }}{\text { Water }}=\Large\frac{3}{7}\right\rangle 10 \text { units }\\
\text{In Mixture -2 ratio of}\\
\left.\Large\frac{\text { Spirit }}{\text { Water }}=\Large\frac{7}{5}\right\rangle 12 \text { units }\end{array}$
$\begin{array}{l}\text{10 units →20 litres}\\ \text{1 unit →2 litres}\\ \text{12 units →36 litres}\\ \text{1 unit →3 litres}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -1}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{3 \times 2}{7 \times 2}=\frac{6}{14}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -2}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{7 \times 3}{5 \times 3}=\frac{21}{15}\end{array}$
$\begin{aligned}&\text{Ratio of spirits and water}\\ &=\frac{6+21}{14+15} \\ &=\frac{27}{29} \\ &=27: 29 \end{aligned}$
$\begin{array}{l}\text{10 units →20 litres}\\ \text{1 unit →2 litres}\\ \text{12 units →36 litres}\\ \text{1 unit →3 litres}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -1}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{3 \times 2}{7 \times 2}=\frac{6}{14}\end{array}$
$\begin{array}{l}\therefore\ \text{In Mixture -2}\ \text{ratio of}\\ \Large\frac{\text { Spirit }}{\text { Water }}=\frac{7 \times 3}{5 \times 3}=\frac{21}{15}\end{array}$
$\begin{aligned}&\text{Ratio of spirits and water}\\ &=\frac{6+21}{14+15} \\ &=\frac{27}{29} \\ &=27: 29 \end{aligned}$
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