Question

The monthly salary of a person is Rs. 12,000 and his monthly expenditure is Rs. 8,500. Find the ratio of his
(i) Salary to Expenditure
(ii) Expenditure to Savings
(iii) Savings to Salary

Answer 1

Hint: We will consider all the options separately and calculate all the ratios separately. The ratio of two numbers is given by a:b where a and b are two numbers. The ratio on the simplest form is the last fraction (after dividing all the possible terms). Savings can be obtained by subtracting the expenditure from the salary.

Complete step-by-step solution:
We are given the monthly salary of the person as Rs. 12,000.
\[\Rightarrow \text{Salary}=Rs.12000\]
And his monthly expenditure is Rs. 8,500.
\[\Rightarrow \text{Expenditure}=Rs.8500\]
Savings can be obtained by subtracting the expenditure from the salary. Therefore, the saving will be
\[\text{Savings}=\text{Salary}-\text{Expenditure}\]
Substituting the values of salary and expenditure, we get,
\[\Rightarrow \text{Savings}=Rs.12000-Rs.8500\]
\[\Rightarrow \text{Savings}=Rs.3500\]
Therefore, the savings will be Rs. 3500.
Let us consider part (i) salary to expenditure. The ratio of salary to expenditure is given by
\[\dfrac{\text{Salary}}{\text{Expenditure}}=\dfrac{Rs.12000}{Rs.8500}\]
\[\Rightarrow \dfrac{\text{Salary}}{\text{Expenditure}}=\dfrac{120}{85}\]
\[\Rightarrow \dfrac{\text{Salary}}{\text{Expenditure}}=\dfrac{24}{17}\]
Therefore, the ratio of the salary to expenditure is \[\dfrac{24}{17}.\]
Now, consider part (ii) expenditure to savings. The ratio of the expenditure to savings is given by
\[\dfrac{\text{Expenditure}}{\text{Savings}}=\dfrac{8500}{3500}\]
\[\Rightarrow \dfrac{\text{Expenditure}}{\text{Savings}}=\dfrac{85}{35}\]
\[\Rightarrow \dfrac{\text{Expenditure}}{\text{Savings}}=\dfrac{17}{7}\]
Therefore the ratio of the expenditure to savings is given by \[\dfrac{17}{7}.\]
Now, let us consider part (iii) savings to salary. The ratio of the savings to salary is given by
\[\dfrac{\text{Savings}}{\text{Salary}}=\dfrac{3500}{12000}\]
\[\Rightarrow \dfrac{\text{Savings}}{\text{Salary}}=\dfrac{35}{120}\]
\[\Rightarrow \dfrac{\text{Savings}}{\text{Salary}}=\dfrac{7}{24}\]
So the ratio of savings to salary is \[\dfrac{7}{24}.\]
Hence, we have obtained the answers as
\[\left( i \right)\dfrac{24}{17}\]
\[\left( ii \right)\dfrac{17}{7}\]
\[\left( iii \right)\dfrac{7}{24}\]

Note: The ratio when the numerator is greater than the denominator implies that the value of the numerator is greater than the denominator. For example, if the ratio of savings to salary is \[\dfrac{7}{24},\] as the numerator is less and the denominator is greater, the value of the denominator is greater. Also, we can generalize as the ratio is greater than 1, the numerator is bigger and the ratio less than 1, the denominator will be bigger.