In a solution the ratio of mik and water is 3:4, If 40 litres of mixture is taken out and 18 litres milk is added to the mixture, then the percentage of water in the mixture becomes 14*2/7%. What is the total volume of the initial mixture ?
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given ratio of milk and water = 3:4
hence, milk = 3x and water = 4x (let)
total mixture = 3x + 4x = 7x
now,
40 litre of mixture is taken out and 18 litre milk is added
volume of total mixture = 7x - 40 + 18
= 7x - 22
milk in 40 litre = (3/7)*40 = 120/7
water in 40 litre = (4/7)*40 = 160/7
milk in new mixture = 3x - 120/7 + 18
= 3x + 6/7
water in new mixture = 4x - 160/7
percentage of water in new mixture = 100/7
=(4x-160/7)(7x-22)*100 = 100/7
(28x - 160)/7(7x - 22) = 1/7
28x - 160 = 7x - 22
28x - 7x = 160 - 22
21x = 138
x = 138/21
= 46/7 litre
total volume of initial mixture
= 7x
= 7*46/7
= 46 litre.
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