Question

A man donated \[5\% \] of his income to a charitable organization and deposited \[20\% \] of the remainder in the bank. Now if he has \[Rs.{\text{ }}1919\] left, what is his income?

Answer 1

Hint: To solve this question, we will start with assuming the total income of the man to be x. Then we will find all the values in terms of x. He donated \[5\% \] of his income, so we will find the amount left with him after donating. Then he deposited \[20\% \] of the remainder in the bank, so we will find the amount left with him and compare with the given information and hence we will make a linear equation. After finding the value of x, we will get our required answer.

Complete step-by-step answer:
We have been given that a man donated \[5\% \] of his income to a charitable organization and deposited \[20\% \] of the remainder in the bank. It is given that now he has \[Rs.{\text{ }}1919\] left, so we need to find his income.
Let the income of man be x.
So, we have been given that he donated \[5\% \] of his income to a charitable organization.
Therefore, donation made by him $ = \dfrac{{5x}}{{100}}$
Now, the money left with him $ = x - \dfrac{{5x}}{{100}}$
$ = \dfrac{{95x}}{{100}}$
We have also been given that he deposited \[20\% \] of the remainder in the bank.
 Therefore, money deposited by him in the bank $ = \dfrac{{20}}{{100}}(\dfrac{{95x}}{{100}})$
 So, now the total money left with him $ = \dfrac{{95x}}{{100}}(\dfrac{{80}}{{100}})$
But it is given that he has \[Rs.{\text{ }}1919\] left.
So, on comparing the amount he left with, we get
$\dfrac{{95x}}{{100}}(\dfrac{{80}}{{100}}) = 1919$

$
   \Rightarrow x = \dfrac{{100 \times 100 \times 1919}}{{80 \times 95}} \\
  x = \dfrac{{20 \times 20 \times 1919}}{{16 \times 19}} \\
  x = 2525 \\
 $
Thus, the income of man is \[Rs.{\text{ }}2525.\]

Note: In the solutions, students should note that, we have first found the amount he donated, next we found the amount he left with him. Then he deposited the \[20\% \] of the remainder in the bank, this time we calculated with the money left after giving donation, not with the whole income.