Question

The ratio of income to the savings of a family is $13:4$. Find the expenditure if the savings is Rs. $2700$.

Answer 1

Hint: In the given question ratio of income to the savings is given here we will first use the concept of ratio on multiplying the numerator and denominator of the ratio with a constant there will be no effect after converting the ratio into respective number firstly we find the value of income and savings then find the expenditure
Expenditure= income- savings

Complete step-by-step answer:
Let us assume the ratio of income to the saving as $13x$ and $4x$ and by multiplying the constant $x$ to the numerator and denominator
As we know that the given saving is $2700$ so we equate the $4x$ to $2700$
$4x$ = $2700$
We will divide $2700$ by $4$ we get the value of $x$
$x = \dfrac{{2700}}{4}$
We get the value of as $675$
$x = Rs. 675$
When we substitute $x$ in $4x$ and $13x$ we will get income and savings
$4 \times 675 = 2700$(savings)
$13 \times 675 = 8775$(income)
We will get the expenditure by using formula
Expenditure = Income - Savings
On putting the values in formula we get
Expenditure = $8775 - 2700$
$ = Rs. 6075$
Hence the final answer i.e expenditure is $Rs. 6775$

Additional Information: If the ratio of the two numbers is a:b. Then the numbers can be assumed to be ak and bk, where k is a constant. When all the elements of a ratio are multiplied or divided by the same number. The resulting ratio is equal to the original ratio.

Note: When we have a ratio form for example a:b. Then by multiplying k where k is a constant. Making the numbers as ak and bk. Now form the equation according to the requirement of the question. Students mainly get confused in forming the equation. By equating the equation we will find the value of k students mainly get confused in forming the equation they mainly make mistakes in equating the equation. Many forgets to find the respective values of ratio they just left the question after finding k
Student should read carefully before equating and make sure to find respective values after finding k
Formula to remember: Expenditure= income - savings