Question

$\text{Rohan filled}\frac{4}{10}\text{part of the jug with hot}$

$\text{water and}\frac{17}{100}\text{part of the jug with cold water.}$

Calculate the fraction of the jug that is not filled with water.

• A. $\frac{27}{100}$
• B. $\frac{43}{100}$
• C. $\frac{31}{100}$
• D. $\frac{52}{100}$

Answer 1

The correct option is B $\frac{43}{100}$

$\text{Fraction of the jug filled with hot water =}\frac{4}{10}$

$\text{Fraction of the jug filled with cold water =}\frac{17}{100}$

$\text{Part of jug filled with hot and cold}$
$\text{water =}\frac{4}{10}+\frac{17}{100}$

Let's convert the fractions into like fractions.

$\frac{4}{10}=$ $\frac{4\times 10}{10\times 10}$

$=\frac{40}{100}$

$\text{∴ Part of jug filled with water =}\frac{4}{10}+\frac{17}{100}$
$=\frac{40}{100}+$ $\frac{17}{100}$

$=\frac{40+17}{100}$

$=\frac{57}{100}$

Now, to find the fraction of jug without any water, subtract this fraction from 1.

$\text{∴ Part of the jug not filled with water =}1-\frac{57}{100}$
$=\frac{100}{100}-\frac{57}{100}$

$=\frac{100-57}{100}$

$=\frac{43}{100}$

$\therefore \frac{43}{100}\text{part of the jug is not filled with water.}$