Question

A mixture contains milk and water in the ratio 8 ∶ x. If 3 liters of water is added in 33 liters of mixture, the ratio of milk and water becomes 2 ∶ 1, then value of x is:

• A. 3 Litres
• B. 4 Litres
• C. 2 Litres
• D. 11 Liters

Answer 1

Answer: (A)

3 Litres

Answer 2

$\frac{Milk}{Water} =\frac{ 8}{x}$.

Before water is added, the mixture's entire volume is : $Milk + Water$ = $33$ $liters$.

The ratio of milk to water after adding three liters is $2:1$, therefore $\frac{Milk }{ (Water + 3)} = \frac{2}{1}$.

To determine the values of $Milk(M)$, $Water(W)$, and $x$, we can solve these equations.

Equations (2) and (3) give us:

$M = 2 × (W + 3)$

Substitute $M = 33 - W$ from equation (2) into the above equation, we get:

$33 - W = 2 × (W + 3)$

$33 - W = 2W + 6$

$33 - 6 = 2W + W$

$27 = 3W$

$W = \frac{27 }{ 3} = 9$ $liters$.

Replacing $W = 9$ into equation (1), we get:

$\frac{M }{ 9} = \frac{8 }{ x}$

$M = \bigg(\frac{8}{ x}\bigg) × 9$

$\bigg(\frac{8}{ x}\bigg) × 9 + 9 = 33$

$\bigg(\frac{72 }{ x}\bigg) + 9 = 33$

$\frac{72 }{ x} = 33 - 9 = 24$

cross multiplying, we get:

$x = \frac{72 }{24}$

$x = 3$.

Therefore, x is 3.