Question

Nikhil spent $5\% $ of his monthly income on his children’s education, invested $14\% $ in shares, deposited $3\% $ in a bank and used $40\% $ for his daily expenses. He was left with a balance of Rs. 19,000. What was his income that month?

Answer 1

Hint: We can assume the income of the person to be a variable. Then we can find the money that he spent on each activity using the percentages. Then we can add all the expenditure and the balance money he has equated to the income to get an equation in one variable. On simplification and solving we can solve for the variable to get the total income.

Complete step-by-step answer:
Let us take x as the salary of the person in one month.
It is given that he uses $5\% $ of his income on his children’s education. Then the money spent for it is given by, $5\% \times x = \dfrac{{5x}}{{100}}$.
He invests $14\% $in shares. So, the money he spent on shares is $14\% \times x = \dfrac{{14x}}{{100}}$
It is given that he deposits $3\% $ in a bank and it is given by $3\% \times x = \dfrac{{3x}}{{100}}$
It is also given that he uses $40\% $for his daily expenses. So, the money for his daily expenses is $40\% \times x = \dfrac{{40x}}{{100}}$
After all the expenses, he has a balance of Rs. 19,000.
Therefore, the sum of all the expenditures and the balance money will be equal to the persons salary. So, we can write it as an equation.
$ \Rightarrow \dfrac{{5x}}{{100}} + \dfrac{{14x}}{{100}} + \dfrac{{3x}}{{100}} + \dfrac{{40x}}{{100}} + 19000 = x$
By adding all the fractions, we get,
$ \Rightarrow \dfrac{{62x}}{{100}} + 19000 = x$
We can take the terms containing x to one side.
\[ \Rightarrow x - \dfrac{{62x}}{{100}} = 19000\]
On taking the LCM of the LHS, we get,
\[ \Rightarrow \dfrac{{100x - 62x}}{{100}} = 19000\]
After doing the subtraction, we get,
\[ \Rightarrow \dfrac{{38x}}{{100}} = 19000\]
We can multiply both sides with \[\dfrac{{100}}{{38}}\], we get,
\[ \Rightarrow x = 19000 \times \dfrac{{100}}{{38}}\]
\[ \Rightarrow x = 50,000\]
Therefore, the person's monthly income is Rs. 50000.

Note: Alternate method to solve this problem is given by,
We can take the sum of the percentages of all the expenditures.
\[ \Rightarrow 5\% + 14\% + 3\% + 40\% = 62\% \]
Then the percentage of his balance money is given by $100\% - 62\% = 38\% $
It is given that the balance money he has is Rs. 19,000.
Let x be the person's monthly income. Then \[38\% \] of x is the balance money he has.
$ \Rightarrow \dfrac{{38}}{{100}}x = 19000$
\[ \Rightarrow x = 19000 \times \dfrac{{100}}{{38}}\]
\[ \Rightarrow x = 50,000\]
Therefore, the person's monthly income is Rs. 50000.