Question

A man spends \[78{\text{ }}\% \] of his monthly income and saves \[Rs.{\text{ }}1,100\]. What is his monthly income?

Answer 1

Hint: The relation between income, spending and savings is given as:
\[Savings{\text{ }} = {\text{ }}Income{\text{ }}-Spending\]
We can calculate the monthly income by putting the given information in this equation. Here, the spending of the man is given in percentage form. For example, if a man earns \[Rs.{\text{ }}100\] in a month, and has a spending of \[{\text{6 }}\% \], then he spends \[Rs.{\text{ }}6\] out of his monthly income. We can get an idea to solve this question from this example.


Complete step by step solution:
Savings = \[Rs.{\text{ }}1,100\] and spending is \[78{\text{ }}\% \] of monthly income.
Let us consider the monthly income of the man to be \[Rs{\text{ }}x\] .
Spending \[78\% \; = \dfrac{{78}}{{100}}x\] of monthly income.
We know that, \[Savings{\text{ }} = {\text{ }}Income{\text{ }}-Spending\]
Now putting all the above values in the relation, we get,
\[
  1100 = x - \dfrac{{78}}{{100}}x \\
  1100 = \dfrac{{100x - 78x}}{{100}} \\
  22x = 1100 \times 100 \\
  x = \dfrac{{1100 \times 100}}{{22}} \\
  x = 5000 \\
 \]
Hence the monthly income is \[Rs{\text{ }}5,000\] .


Note: You can consider the spending to be in points, such as \[0.78x\] and then calculate for x. The result will be the same. Sometimes instead of asking to calculate the monthly income, they may ask you to compute the monthly savings or the monthly spending or expenditures. The same relation used above can be applied. You just have to consider what is asked to find as a variable, say x, and solve for x. Don’t try to over compute the calculation part. Understand the difference between income, expenditure and savings.