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 ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Mixture }} - {\text{1 = 20 litres}} \cr & {\text{Mixture }} - {\text{2 = 36 litres}} \cr & {\text{In Mixture }} - {\text{1 ratio of }} \cr & {\text{ }}\frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \left. {\frac{3}{7}} \right\rangle 10{\text{ units}} \cr & {\text{In Mixture }} - 2{\text{ ratio of}} \cr & {\text{ }}\frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \left. {\frac{7}{5}} \right\rangle 12{\text{ units}} \cr & \cr & {\text{10 units }} \to {\text{20 litres}} \cr & \,\,\,{\text{1 unit }}\,\,\, \to {\text{2 litres}} \cr & {\text{12 units }} \to {\text{36 litres}} \cr & \,\,\,{\text{1 unit }}\,\,\, \to {\text{3 litres}} \cr & \cr & \therefore {\text{In Mixture }} - {\text{1 ratio of }} \cr & \frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \frac{{3 \times 2}}{{7 \times 2}} = \frac{6}{{14}} \cr & \cr & \therefore {\text{In Mixture }} - 2{\text{ ratio of }} \cr & \frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \frac{{7 \times 3}}{{5 \times 3}} = \frac{{21}}{{15}} \cr & \cr & {\text{Ratio of spirits and water}} \cr & {\text{ = }}\frac{{6 + 21}}{{14 + 15}} \cr & {\text{ = }}\frac{{27}}{{29}} \cr & {\text{ = 27:29}} \cr} $$