Question

The salary of a person is $20,000$ provident fund is $9\%$ is deducted from the remaining he spends $10\%$ on house rent and $20\%$ on transportation. Find the amount deducted on prominent funds and also find how much money was spent on rent and transportation.

Answer 1

Hint: To solve this question we need to have the knowledge of percentage. There are conditions given in the questions which will help us to find the value for provident fund, money spent in rent and transportation. To solve this problem we will firstly convert the percentage into fraction and then multiply it with the total amount.

Complete step by step answer:
The question asks us to find the money deducted in Provident Fund and spent on rent and transportation if a person gets a salary of $20,000$ in which provident fund is $9\%$ and from the remaining money the amount spent is $10\%$ and $20\%$ respectively.
The first step is to convert the percentage into fraction form. We will find the amount used in the Provident Fund. It will be $\text{9 }\!\!\%\!\!\text{ of 20,000}$. On writing it mathematically we get:
$\Rightarrow \text{9 }\!\!\%\!\!\text{ }\times \text{ 20,000}$
Now we will convert the percentage into fraction, on doing this we get:
$\Rightarrow \dfrac{9}{100}\times \text{ 20,000}$
$\Rightarrow \dfrac{9\times 20,000}{100}$
\[\Rightarrow \text{Rs }1800\]
The amount used in the Provident Fund is $1800$ .
Now the remaining amount left with the person is the difference of the total salary and the amount used in the Provident Fund. On writing it mathematically we get:
$\Rightarrow 20,000-1,800$
$\Rightarrow 18,200$
Now we will calculate the money spent on the rent and the transportation which is $10\%$ and $20\%$ respectively of the remaining amount, which is $\text{Rs 18},200$. The house rent hence will be:
$\Rightarrow 10\%\times 18,200$
Now we will convert the percentage into fraction, on doing this we get:
$\Rightarrow \dfrac{10}{100}\times \text{ 18,200}$
$\Rightarrow \dfrac{10\times 18,200}{100}$
$\Rightarrow 1,820$
The amount used in House Rent is $\text{Rs 1,}820$ .
Now we will calculate the money spent on transportation. The transportation hence will be:
$\Rightarrow 20\%\times 18,200$
Now we will convert the percentage into fraction, on doing this we get:
$\Rightarrow \dfrac{20}{100}\times \text{ 18,200}$
$\Rightarrow \dfrac{20\times 18,200}{100}$
$\Rightarrow 3,640$
The amount used in transportation is $\text{Rs 3,64}0$ .
$\therefore $ The amount used in Provident Fund is $1800$, House Rent is $\text{Rs 1,}820$ and transportation is $\text{Rs 3,64}0$

Note: The percentage is changed to fraction for the calculation purpose. The percentage is a fraction in terms of $100$. So to convert the percentage into fraction the percentage value is divided by $100$. For example if we are given $p\%$ then the fractional form will be $\dfrac{p}{100}$ .