Question

The ratio of income to expenditure of a family is 7:6. Find the saving if the income of the family is Rs. 42000?

Answer 1

Hint: Start with assuming income and expenditure as some variables satisfying the ratio given. Use the value of income given in the question to find the ratio variable and hence find the expenditure using that variable. Savings will be the difference between income and expenditure.
Income = saving + Expenditure

Complete step-by-step answer:
Let us consider income to be 7x and expenditure be 6x.
According to the question, Income=7x=42000
Now, we will calculate the value of x:
According to the question, we have:
$7{\text{x = 42000}}$
$
   \Rightarrow x = \dfrac{{42000}}{7} \\
  \therefore x = 6000 \\
  $
As, we have assumed Expenditure= $6x$
So, we will get the value of expenditure by putting the value of x :
  So, Expenditure = $6x$
   Expenditure = \[ 6 \times 6000 \] Expenditure = $36000$
Now, as we know that income is the sum of savings and expenditure.
i.e., Income = Saving + Expenditure
      Savings = Income - Expenditure
Now, putting the value of income and expenditure, we have:
$
  Savings = Rs 42000 - Rs 36000
  \therefore Savings = Rs 6000
  $

Thus, the savings of the family is Rs6000.

Note: This problem can be solved using fractions. It is given in question that the 7th part of the income equals Rs42000.
So, its $1^{st}$ part comes out to be $ \dfrac{{42000}}{{7}} = 6000.$
Then ,we can calculate the expenditure by calculating its 6th part i.e. , 6x6000=36000.
We know that saving is the difference between income and expenditure.
So, savings=$7^{st}$ part-$6^{st}$ part= $1^{st}$ part =6000.