A mixture has milk and water in the ratio 4: 1. When 50% of the mixture is taken out and replaced by 24 liters of water then the ratio of milk to water in the mixture becomes 1: 1. Find initial quantity of mixture.

Let initial quantity of milk and water in the mixture be ’40x liters’ and ’10x liters’ respectively.

ATQ,

$frac{{left( {40{ m{x}} imes frac{1}{2}} ight)}}{{10{ m{x}} imes frac{1}{2} + 24}} = frac{1}{1}$

$frac{{20{ m{x}}}}{{5{ m{x}} + 24}} = frac{1}{1}$

$20{ m{x}} = 5{ m{x}} + 24$

15x = 24

x = 1.6

So, required quantity = 40x + 10x

= 50x

= 80 liters