Question

A man spends $35\% $ of his income on food, $25\% $ on children’s education and $80\% $ of the remaining on house rent. What percent of his income is left?
A) $8 \% $
B) $10 \% $
C) $12 \% $
D) $14 \% $

Answer 1

Hint:
Here, we will find the percentage left on his income at first after spending on food, children’s education. We will then find the percentage of income spent on house rent in terms of the total income. Then, we will find the percentage of income left at the end. Percentage is defined as a ratio representing as a fraction of 100.

Formula Used:
Percentage is given by the formula $P = \dfrac{x}{n} \times 100$.

Complete Step by Step Solution:
Let us consider in Percentage, the total income of a man is $100\% $. Then,
Percentage of his income spent on food $ = 35\% $
Percentage of his income spent on children’s education $ = 25\% $
Now, we will find the percentage left on his income.
The percentage left on his income is found by adding the percentage spent on food and children’s education and subtracting it from the Total Income.
 Percentage left on his income $ = $ Total Income $ - $ (Percentage spent on food $ + $ Percentage spent on children’s education)
Now substituting the values in the above equation, we get
$ \Rightarrow $ Percentage left on his income $ = 100\% - \left( {35\% + 25\% } \right)$
Adding the terms in the bracket, we get
$ \Rightarrow $ Percentage left on his income $ = 100\% - \left( {60\% } \right)$
$ \Rightarrow $ Percentage left on his income $ = 40\% $
Now, we will find the Percentage spent on house rent in terms of total income. We are given that $80\% $ of the remaining on house rent.
Percentage spent on house rent in terms of total income is found by multiplying the Percentage spent on house rent of the remaining with the percentage left on his income.
Percentage Spent on house rent $ = \dfrac{{80}}{{100}} \times 40$
Dividing the terms, we get
 $ \Rightarrow $ Percentage Spent on house rent $ = 8 \times 4$
Multiplying the terms, we get
$ \Rightarrow $ Percentage Spent on house rent $ = 32\% $
Thus the man spent $32\% $ on house rent.
Now, we will find the percentage left on his income.
Percentage left on his income is found by subtracting the percentage spent on house rent from the percentage left on his income at first.
Percentage left on his income $ = $ Percentage left on his income at first $ - $ Percentage spent on house rent.
Substituting the values of percentage in the above equation, we get
$ \Rightarrow $ Percentage left on his income $ = 40\% - 32\% $
$ \Rightarrow $ Percentage left on his income $ = 8\% $
Therefore, a man has left with $8\% $ of his income.

Thus option (A) is the correct answer.

Note:
We need to keep in mind that if the given values are in percentage, then the total of the value becomes 100 automatically because the percentage represents a fraction by 100. Percentage on house rent is given for the income left after spending on food and children’s education but we may consider it for the income at first. This may cause a mistake in finding the percentage left on his income.