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

The Correct Option is A

\(\frac{Milk}{Water} =\frac{ 8}{x}\).

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.