Question

Milk is mixed with $\frac{1}{8}$ part of water in a bottle, so that the mixture becomes $\frac{5}{6}$ parts of the bottle. Amount of milk added is .

• A. $\frac{17}{22}$
• B. $\frac{17}{24}$
• C. $\frac{19}{24}$
• D. $\frac{19}{22}$

Answer 1

The correct option is B $\frac{17}{24}$

Fraction of water = $\frac{1}{8}$

Fraction of milk mixture
= Fraction of milk + Fraction of water
= $\frac{5}{6}$

Fraction of milk added
= Amount of mixture - Amount of water
= $\frac{5}{6}$ - $\frac{1}{8}$

Since the denominator are not the same, we have to convert these into like fractions.

First, let's see whether 6 is a factor of 8.

Let's find the common multiple of 6 and 8.
24 is the first common multiple of 6 and 8.

$\therefore$ Milk added = $\frac{5\times 4}{6\times 4}$ - $\frac{1\times 3}{8\times 3}$
= $\frac{20}{24}$ - $\frac{3}{24}$
= $\frac{17}{24}$

Therefore, the fraction of milk added is $\frac{17}{24}$.