Question

Total income of Ramesh, Suresh, and Preeti is 8, 07, 000 rupees. The percentage of their expenses are $75\%,80\%$ and $90\%$ respectively. If the ratio of their savings is $16:17:12$, then find the annual savings of each of them?

Answer 1

Hint: First of all, we are going to convert the ratio of the savings of incomes of Ramesh, Suresh, and Preeti into numbers by multiplying each of the ratio with x and then the savings of them are $16x,17x\And 12x$ respectively. We know that the formula for the percentage of savings is equal to the subtraction of expenses percentage from 100 so we are going to use the formula and find the savings percentage of Ramesh, Suresh, and Preeti. After that, we are going to use the savings percentage formula which is equal to $Savings\%=\dfrac{Savings}{Income}\times 100$. From this formula, we can find the savings of each of Ramesh, Suresh, and Preeti.

Complete step-by-step solution:
The ratio of the savings of Ramesh, Suresh, and Preeti is given as follows:
$16:17:12$
Now, we are going to convert the above ratio into a number by multiplying each of the ratio numbers by x and we get,
The savings of Ramesh, Suresh and Preeti are $16x,17x\And 12x$ respectively.
We know that the percentage of savings is equal to the subtraction of expenses percentage from 100.
Percentage of savings of Ramesh is equal to:
$\begin{align}
  & 100-75 \\
 & =25\% \\
\end{align}$
Percentage of savings of Suresh is equal to:
$\begin{align}
  & \left( 100-80 \right)\% \\
 & =20\% \\
\end{align}$
Percentage of savings of Preeti is equal to:
$\begin{align}
  & \left( 100-90 \right)\% \\
 & =10\% \\
\end{align}$
Now, we know the formula for savings percentage is equal to:
$Savings\%=\dfrac{Savings}{Income}\times 100$
Substituting the savings percentage, savings value for Ramesh in the above formula we get,
$\begin{align}
  & 25=\dfrac{16x}{Income}\times 100 \\
 & \Rightarrow Income=\dfrac{100\left( 16x \right)}{25} \\
 & \Rightarrow Income(\text{of Ramesh})=64x \\
\end{align}$
Similarly, we can find the income of Suresh and Preeti also.
Income of Suresh is calculated as follows:
$\begin{align}
  & 20=\dfrac{17x}{Income}\times 100 \\
 & \Rightarrow Income=\dfrac{100\left( 17x \right)}{20} \\
 & \Rightarrow Income(\text{of Suresh})=85x \\
\end{align}$
Income of preeti is calculated as follows:
$\begin{align}
  & 10=\dfrac{12x}{Income}\times 100 \\
 & \Rightarrow Income=\dfrac{100\left( 12x \right)}{10} \\
 & \Rightarrow Income(\text{of Preeti})=120x \\
\end{align}$
Now, the addition of Ramesh, Suresh and Preeti is equal to Rs. 8, 07, 000 so adding these three incomes and we get,
$\begin{align}
  & 64x+85x+120x=807000 \\
 & \Rightarrow 269x=807000 \\
 & \Rightarrow x=\dfrac{807000}{269}=3000 \\
\end{align}$
Substituting the above value of x in $16x,17x\And 12x$ we get,
Savings of Ramesh is equal to:
$\begin{align}
  & 16\left( 3000 \right) \\
 & =Rs48000 \\
\end{align}$
Savings of Suresh is equal to:
$\begin{align}
  & 17\left( 3000 \right) \\
 & =Rs51000 \\
\end{align}$
Savings of Preeti is equal to:
$\begin{align}
  & 12\left( 3000 \right) \\
 & =Rs36000 \\
\end{align}$
Hence, we have found savings for Ramesh, Suresh, and Preeti.

Note: To solve the above problem, we must know the concept of savings, expense, and income. If we know this concept then it would be quite easy to solve this problem. Also, you should know the formula for savings percentage formula with respect to savings and income.