Question

A milk vender has two cans c1 and c2 of capacity of 300 litres each.both the cans are full to the brim with milk-water solution.the concentration of milk in c1 is 75% and that in c2 is 50%.how much quantity of solution should the vender mixture from the c1 and c2 sunch that he gets 180 litre of solution having water and milk in the ratio of 3:5?

Answer 1

Let x and (12-x) litres of milk be mixed from the first and second container respectively

Amount of milk in x litres of the the first container = .75x

Amount of water in x litres of the the first container = .25x

Amount of milk in (12-x) litres of the the second container = .5(12-x)

Amount of water in (12-x) litres of the the second container = .5(12-x)

Ratio of water to milk = [.25x + .5(12-x)] : [.75x + .5(12-x)] = 3 : 5

⇒ ( .25 x + 6 − .5 x )

( .75 x + 6 − .5 x )

= 3 5

⇒ ( 6 − .25x)

( .25 x + 6 )

= 3 5

30 − 1.25 x

= .75 x + 18

⇒ 2 x = 12

⇒ x = 6

Since x = 6, 12-x = 12-6 = 6

Hence 6 and 6 litres of milk should mixed from the first and second container respectively