Question

Q: A vessel contains milk and water
in the ratio 3:5. When 6 litres of this
solution is removed and replaced
with water, the ratio of milk and
water becomes 5:9. How many litres
of the solution was present in the
vessel originally?​

Answer 1

Answer: 126 litres, 210 litres

Explanation:

Let the quantity of milk and water be x and 3x.

According to the question,

$\sf{ \dfrac{3x - 6}{5x + 6} = \dfrac{5}{9} }$

On cross multiplying,

$\to \sf{9(3x-6) = 5(5x+ 6)}$

$\hookrightarrow \: \sf{27x - 54 = 25x + 30}$

$\implies \sf{27x - 25x= 30 + 54}$

$\sf{ \implies 2x = 84}$

$\bf{ \implies x = 42}$

Substitute the value of x in the given ratio to find out the value of y.

• 3x = 3(42) = 126
• 5x = 5(42) = 210

∴ The initial volume of milk and water is 126 Litres and 210 litres respectively.