Question

The monthly income of a person was Rs.13500 and his monthly expenditure was Rs.9000. Next year, his income increases by 14% and his expenditure by 7%. What was the percentage increase in his saving?
A.18%
B.32%
C.21%
D.None of these

Answer 1

Hint: The relation between income, spending and savings is given as: \[Savings{\text{ }} = {\text{ }}Income{\text{ }}-Spending\]
In this question the income and expenditure of the person, hence his saving can be calculated and since it is said that his income and expenditure both have increased, therefore find his new increased income and increased expenditure by using increase in percent formula to find his new savings.
Percent increase is the measure of percent change, which is extended to which something gains value. Where Increase= New number – Original number, whereas

Complete step-by-step answer:
Present monthly Income,\[{I_1} = Rs.13500\]
Present monthly Expenditure, \[{E_1} = Rs.9000\]
Since the monthly expenditure of the person is less than his expenditure then the person has the savings, given by
Present Saving= Present monthly Income - Present monthly Expenditure
\[Saving,{S_1} = 13500 - 9000 = Rs.4500\]
As income of the person has increased by 14%, hence the income of the person for next year
\[
  {I_2} = Rs13500 + \dfrac{{14}}{{100}} \times 13500 \\
   = 13500 + 1890 \\
   = Rs.15390 \\
 \]
Also, the expenditure of the person has increased by 7%, therefore his new expenditure
\[
  {E_2} = Rs9000 + \dfrac{7}{{100}} \times 9000 \\
   = 9000 + 630 \\
   = Rs.9630 \\
 \]
So the saving of the person of next year will be
\[
  {S_2} = 15390 - 9630 \\
   = Rs.5760 \\
 \]
Therefore his increase in saving will be
\[
  S = 5760 - 4500 \\
   = Rs.1260 \\
 \]
So the increase in percentage of saving \[ = \dfrac{{Saving}}{{OriginalIncome}} = \dfrac{{1260}}{{4500}} \times 100 = 28\% \]
So, the correct answer is “Option D”.

Note: Students should consider the monthly income as any variable. Also, the relation between income, spending and savings must be kept in mind. 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.