Vessel A contains a mixture of milk and water and vessel B contains a mixture of 240 liters mixture of milk and water in the ratio of 7:5 and the total quantity of vessel A and 60% of the mixture of vessel B are mixed together in a new empty vessel, then the ratio of the milk to water becomes 6:5. Find the ratio of the quantity of milk to water in vessel A initially, if the quantity of milk in vessel A is 4 liters less than that of water in vessel A.
a) 8:7
b) 5:4
c) 9:10
d) 4:5
e) None of these
Sol:
Let the quantity of milk and water in vessel A is x
and (x + 4) liters respectively.
60% of the quantity of mixture in vessel B = 240 *
60/100 = 144 liters
(x + 144 * 7/12)/(x + 4 + 144 * 5/12) = 6/5
(x + 84)/(x + 4 + 60) = 6/5
(x + 84)/(x + 64) = 6/5
5x + 420 = 6x + 384
x = 36 liters
Quantity of milk in vessel A = 36 liters
Quantity of water in vessel A = 36 + 4 = 40 liters
Required ratio = 36:40 = 9:10
