Question

in a mixture of 70 litres, the ratio of milk to water is 5:2. if some quantity of mixture is taken out and 7 litres of milk and 7 litres of water are added to the mixture then the ratio of milk to water becomes 7:4. find the quantity of mixture which was taken out initially

Answer 1

Ratio of milk and water in 70 litres of mixture = 5:2
Quantity of milk initially = $\frac{5}{7}$×70 = 50 litres
Quantity of water initially = $\frac{2}{7}$×70 = 20 litres

Let us assume x litres of mixture was removed.
After removal and adding 7 litres of milk and water
Quantity of milk = 50 - $\frac{5x}{7}$ +7
Quantity of water = 20 -$\frac{2x}{7}$ +7
Hence,$\frac{50- \frac{5x}{7} +7 }{20- \frac{2x}{7}+7 } = \frac{7}{4}$
=>200 - $\frac{20x}{7}$ + 29 = 140 -2x +49
=> 228 - 189 = $\frac{20x}{7}$ - 2x
=> $\frac{6x}{7} = 39$
=> x = 45.5 litres
Ans: Quantity of mixture taken out initially was 45.5 litres.