Three containers A, B and C are having mixtures of milk and water in t

1.	Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7 respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together. (a) 51 : 115 (b) 52 : 115 (c) 53 : 115 (d) 54 :115
Answer» (c) 53 : 115 Ratio of milk and water = \(\big(\frac16\times5+\frac38\times4+\frac{5}{12}\times5\big)\) : \(\big(\frac56\times5+\frac58\times4+\frac{7}{12}\times5\big)\) = \(\big(\frac56+\frac32+\frac{25}{12}\big)\) : \(\big(\frac{25}6+\frac52+\frac{35}{12}\big)\) = \(\big(\frac{10+18+25}{12}\big)\): \(\big(\frac{50+30+35}{12}\big)\) = \(\frac{53}{12}:\frac{115}{12}\) = 53 : 115

Three containers A, B and C are having mixtures of milk and water in the ratio 1 : 5, 3 : 5 and 5 : 7 respectively. If the capacities of the containers are in the ratio 5 : 4 : 5, then find the ratio of the milk to the water if the mixtures of all the three containers are mixed together. (a) 51 : 115 (b) 52 : 115 (c) 53 : 115 (d) 54 :115

Answer»

(c) 53 : 115

Ratio of milk and water

= \(\big(\frac16\times5+\frac38\times4+\frac{5}{12}\times5\big)\) : \(\big(\frac56\times5+\frac58\times4+\frac{7}{12}\times5\big)\)

= \(\big(\frac56+\frac32+\frac{25}{12}\big)\) : \(\big(\frac{25}6+\frac52+\frac{35}{12}\big)\)

= \(\big(\frac{10+18+25}{12}\big)\): \(\big(\frac{50+30+35}{12}\big)\)

= \(\frac{53}{12}:\frac{115}{12}\) = 53 : 115