Question

The ratio of income to the expenditure of a family is 7 : 6. Find the savings if the income is Rs. 14000.

Answer 1

Hint: Here the ratio of \[\dfrac{Income}{Expense}=\dfrac{7}{6}\]is applied first. Then, next replace income with Rs. 14000, then solve for the expense. After the expense, we can use the formula \[Income=Expense+Saving\], to obtain the savings.

Complete step-by-step answer:
In the question, we have been given that the ratio of income to the expenditure of a family is 7 : 6, also if the income is Rs. 14000, then we have to find the savings. Now, when the ratio of income to the expenditure is given as 7 : 6, then the equation that we will get will be as follows:
\[\dfrac{Income}{Expense}=\dfrac{7}{6}\]
Next, we are given that income is Rs. 14000, so when we put this income value in the above equation, we can solve to find the expense, as shown below:
\[\begin{align}
  & \Rightarrow \dfrac{1400}{Expense}=\dfrac{7}{6} \\
 & \Rightarrow 6\times 1400=7\times Expense\,\,\,\,\,\,\,\,\left[ Cross\,\,Multiplication \right] \\
 & \Rightarrow \dfrac{6\times 1400}{7}=Expense \\
 & \Rightarrow Expense=6\times 200 \\
 & \Rightarrow Expense=1200 \\
\end{align}\]
So here we get the expense as Rs 1200. Now since we have to find the savings, we know the income and the expense. Also, we know the formula that gives the relation between income, saving and the expense as: \[Income=Expense+Saving\]
So here we are just required to put the value of income and expense so as to obtain the savings. So we get:
\[\begin{align}
  & \Rightarrow Income=Expense+Saving \\
 & \Rightarrow 1400=1200+Saving \\
 & \Rightarrow Saving=200 \\
\end{align}\]

So, we get the savings as Rs 200 only. So, this is the required answer.

Note: We have to be careful while apply the ratio\[\dfrac{Income}{Expense}=\dfrac{7}{6}\] and this should be written as \[\dfrac{Expense}{Income}\ne \dfrac{7}{6}\], as we are given with the ratio of income to the expenditure, so income will come in the numerator and the expense will come in the denominator. Also, to check your calculations we need to make sure that the expanse is not greater than the income, if that happens then there is some calculation error.