Question

A man donated $\dfrac{1}{10}^{th}$ of his money to a school, $\dfrac{\text{1}}{\text{6}}^{th}$ of the remaining to a church and the remaining money he distributed equally among his three children. If each child gets $\text{Rs 50},000$, how much money did the man originally have?

Answer 1

Hint: To solve this question we need to have a knowledge of fraction and operations on fraction. In the first step we will firstly take an assumption which indicates the total money the man originally has is $x$. Then we will be calculating the process as per the conditions given in the question.
The question ask us to find the amount of money the man gets, if he donates $\dfrac{1}{10}$ of his money to a school, $\dfrac{\text{1}}{\text{6}}^{th}$ of the remaining to a church and the remaining money is distributed equally among three children with $\text{Rs 50},000$.

Complete step by step answer:
The first step is to take an assumption where we will assume the total amount the man got to be $x$.
Amount of money donated at school is one- tenth of the money the man gets. On writing it mathematically we get:
$\Rightarrow \dfrac{1}{10}\times x$
$\Rightarrow \dfrac{x}{10}$
Now the amount left with the man after the donation in the school will be:
$\Rightarrow x-\dfrac{x}{10}$
$\Rightarrow \dfrac{9x}{10}$
The second condition given to us is that one- sixth of the remaining money is donated in the church. So the mathematical representation of the above statement will be:
$\Rightarrow \dfrac{1}{6}\times \dfrac{9x}{10}$
$\Rightarrow \dfrac{3x}{20}$
Now the amount of money he is left with is:
$\Rightarrow \dfrac{9x}{10}-\dfrac{3x}{20}$
$\Rightarrow \dfrac{18x}{20}-\dfrac{3x}{20}$
$\Rightarrow \dfrac{18x-3x}{20}$
$\Rightarrow \dfrac{15x}{20}$
$\Rightarrow \dfrac{3x}{4}$
Amount of money each student will get be:
$\Rightarrow \dfrac{1}{3}\times \dfrac{3x}{4}$
$\Rightarrow \dfrac{x}{4}$
The amount of money each student gets is $\text{Rs 50},000$as given in the question. So we will equate the two and will find the value for $x$.
$\Rightarrow \dfrac{x}{4}=50,000$
$\Rightarrow x=4\times 50,000$
$\Rightarrow x=Rs2,00,000$
$\therefore $The money the man originally made is $Rs2,00,000$.

Note: To solve these kinds of questions we always need to take an assumption so that the calculation becomes easy. We can even check whether the answers are correct or not by adding all the amount donated. If the total money sum up to $Rs2,00,000$ then the answer will be correct.