Question

Two mixtures A and B contain milk and water in the ratio 4:5 and 7:4, respectively. In what ratio should the two mixtures be mixed to obtain a new mixture having 55% milk?

• A. 5:7
• B. 7:9
• C. 9:11
• D. 11:13

Hint:

When mixing two mixtures, use the method of allegation to find the ratio of mixing.

Answer 1

The Correct Option is C

Let the quantities of mixtures A and B to be mixed be \( x \) and \( y \), respectively. The amount of milk in mixture A is \( \frac{4}{9} \times x \) and the amount of milk in mixture B is \( \frac{7}{11} \times y \). We want the new mixture to contain 55% milk, so: \[ \frac{\frac{4}{9} \times x + \frac{7}{11} \times y}{x + y} = 0.55. \] Multiplying both sides by \( x + y \) and simplifying the equation, we get: \[ \frac{4}{9}x + \frac{7}{11}y = 0.55(x + y). \] Solving this, we get the ratio \( \frac{x}{y} = \frac{9}{11} \). Thus, the required ratio of mixing the two mixtures is 9:11, which corresponds to option (3).