Sarika spent $\frac{2}{5}$ of her money on buying skirt. She then spent $\frac{4}{9}$ of her remaining money on a belt. What fraction of her money was left?

Given: Sarika spent $\frac{2}{5}$ of her money on buying skirt. She then spent $\frac{4}{9}$ of her remaining money on a belt.

To find: Fraction of her money left with her after buying skirt and belt.

Solution:

Let the total money sarika had with her at the start = a

First she spent $\frac{2}{5}$ of her money on skirt:

Money spent by sarika on skirt = $\frac{2}{5} a$

So,

Money left with sarika = Total money she had $-$ Money spent by her on skirt 

Money left with sarika = $a\ -\ \frac{2a}{5}$

Money left with sarika = $\frac{5a\ -\ 2a}{5}$

Money left with sarika = $\frac{3a}{5}$

Now, she then spent $\frac{4}{9}$ of her remaining money on a belt:

Money spent by sarika on belt = $\frac{3a}{5} \ \times \ \frac{4}{9} \ =\ \frac{12a}{45}$

So,

Money left with sarika = Total money she had after buying skirt $-$ Money spent by her on belt

Money left with sarika = $\frac{3a}{5} \ -\ \frac{12a}{45}$

Money left with sarika = $\frac{27a\ -\ 12a}{45}$

 Money left with sarika = $\frac{15a}{45}$

 Money left with sarika = $\frac{a}{3}$

Therefore, sarika had $\frac{1}{3}$ of her money left with her.

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Updated on: 10-Oct-2022

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