Question

Sarwan spends 20% of his monthly salary on food, 40% of the remaining on house rent and the balance amount spends on the other items of routine expenses. What is his yearly salary if he spends Rs. 5760 per month on other items of routine expenses?
(a) Rs. 120000
(b) Rs. 244000
(c) Rs. 144000
(d) Rs. 154000

Answer 1

Hint: We solve this problem by assuming the monthly salary of Sarwan as some variable. Then we use the conditions that he spends 20% of his monthly salary on food, 40% of the remaining on house rent and the balance amount spends on the other items of routine expenses to find the monthly salary.
We use the condition that the sum of all expenses in a month will be equal to the monthly salary.
We also have the condition that \[x\%\] of \[n\] is given as \[\dfrac{x}{100}\times n\]
Then we find the yearly salary by multiplying the monthly salary with 12 because a year has 12 months.

Complete step by step answer:
Let us assume that the monthly salary of Sarwan as \[S\]
We are given that he spends 20% of his monthly on food.
Let us assume that the amount spent on food as \[F\]
We know that the condition that \[x\%\] of \[n\] is given as \[\dfrac{x}{100}\times n\]
By using the above condition we get the amount spent on food as
\[\begin{align}
  & \Rightarrow F=\dfrac{20}{100}\times S \\
 & \Rightarrow F=\dfrac{S}{5} \\
\end{align}\]
We are given that he spends 40% of remaining money on house rent
Let us assume that remaining amount after spending on food as \[R\] then we get
\[\begin{align}
  & \Rightarrow R=S-\dfrac{S}{5} \\
 & \Rightarrow R=\dfrac{4S}{5} \\
\end{align}\]
Now, let us assume that the amount spent on house as \[H\] then by using the percentage condition we get
\[\begin{align}
  & \Rightarrow H=\dfrac{40}{100}\times R \\
 & \Rightarrow H=\dfrac{2}{5}\times \dfrac{4S}{5} \\
 & \Rightarrow H=\dfrac{8S}{25} \\
\end{align}\]
We are given that he spends Rs. 5760 on other expenses.
Let us assume that the amount spent on other expenses as
\[\Rightarrow E=5760\]
We know that the condition that sum of all expenses in a month will be equal to a monthly salary.
By converting the above statement in to mathematical equation we get
\[\Rightarrow S=F+H+E\]
Now, by substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow S=\dfrac{S}{5}+\dfrac{8S}{25}+5760 \\
 & \Rightarrow S=\dfrac{5S+8S}{25}+5760 \\
 & \Rightarrow S-\dfrac{13S}{25}=5760 \\
 & \Rightarrow \dfrac{12S}{25}=5760 \\
\end{align}\]
Now, by cross multiplying the terms in the above equation we get
\[\begin{align}
  & \Rightarrow S=5760\times \dfrac{25}{12} \\
 & \Rightarrow S=12000 \\
\end{align}\]
Now, let us assume that the yearly salary of Sarwan as \[I\]
We know that the yearly salary is obtained by multiplying the monthly salary with 12 because a year has 12 months.
By using the above statement we get the yearly salary as
\[\begin{align}
  & \Rightarrow I=S\times 12 \\
 & \Rightarrow I=12000\times 12 \\
 & \Rightarrow I=144000 \\
\end{align}\]
Therefore we can conclude that the yearly salary of Sarwan is Rs. 144000
So, option (c) is correct answer.


Note:
 Students may do mistakes in taking the amount spent on the house.
We are given that he spends 40% of the remaining on house rent.
Here the remaining indicates that amount left after spending on food so, we get the amount spend on house as
\[\begin{align}
  & \Rightarrow H=\dfrac{40}{100}\times R \\
 & \Rightarrow H=\dfrac{2}{5}\times \dfrac{4S}{5} \\
 & \Rightarrow H=\dfrac{8S}{25} \\
\end{align}\]
But students may mistake and assume that 40% of the salary and take the amount spent on house as
\[\begin{align}
  & \Rightarrow H=\dfrac{40}{100}\times S \\
 & \Rightarrow H=\dfrac{2S}{5} \\
\end{align}\]
This gives the wrong answer. So, we need to check the question correctly and proceed for the solution.