Question

Out of her total income, Poonam spends 23 % on house rent and 60 % on the rest on household expenses. If she saves Rs. 2100. What is her total income?

Answer 1

Hint: We can find the expression for the amount she saves (by letting a variable as income) and equate it to the amount she saves as given to find the value of total income.
Percentage in terms of a fraction can be written as:
$a\% = \dfrac{a}{{100}}$

Complete step-by-step answer:
Let her total income be 100 x.
Spent on house rent = 23 %
=$\dfrac{{23}}{{100}} \times 100x$
= 23 x
Remaining income = 100 x – 23 x
 Remaining income = 77 x
Spent on household = 60 % of the remaining income
This means 40 % of the remaining income is saved which is given as
$\dfrac{{40}}{{100}} \times 77x$ ___________ (1)
Money saved = Rs. 2100 (Given) ___________ (2)
Equating (1) and (2) as one is the expression for saved money and other is its value, we get:
$\dfrac{{40}}{{100}} \times 77x = 2100$
Calculating for x:
$x = \dfrac{{2100 \times 100}}{{77 \times 40}}$
x = 68.18
Total income = 100 x
 = 68.18 X 100
 = Rs. 6818
Therefore, the total income of Poonam is Rs. 6818

Note: In the cases of percentages, the quantity we let is generally taken as multiple of 100 to make the calculations easier because that multiple gets canceled with 100 in the denominator of the fraction in which the percentage is converted.
Another method to approach can be using:
Total income – Total expenses = Savings
and then substitute the respective values to find the income.