### 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 C

### 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}

## Related Questions On Alligation

A. 2 : 5
B. 3 : 5
C. 5 : 3
D. 5 : 2

### An alloy contains zinc, copper and tin in the ratio 2 : 3 : 1 and another contains copper, tin and lead in the ratio 5 : 4 : 3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in new alloy will be:

A. $\large\frac{1}{2} \mathrm{~kg}$
B. $\large\frac{1}{8} \mathrm{~kg}$
C. $\large\frac{3}{14} \mathrm{~kg}$
D. $\large\frac{7}{9} \mathrm{~kg}$

A. 81 litres
B. 71 litres
C. 56 litres
D. 50 litres