Question

Nine Persons went to a hotel to take their meals. Eight of them spent Rs. 12 each on their meals and the ninth spent Rs. 8 more than the average expenditure of all the nine. What was the total money spent by them?
(a) Rs. 115
(b) Rs. 118
(c) Rs. 120
(d) Rs. 117

Answer 1

Hint: We solve this problem using the given condition by assuming the money spent by the ninth person as some variable and solve for that variable. We use the formula of the average of money as \[\text{Avg}=\dfrac{\text{Sum of money}}{\text{Number of persons}}\]
By using this formula and the condition given that the ninth person spent 8/- more than average we solve for the variable to get total money spent by 9 persons.

Complete step-by-step solution:
Let us assume that the money spent by the ninth person as \['x'\]
We are given that the remaining 8 persons spent Rs. 12 each.
We know that the average money spent is given by formula
\[\text{Avg}=\dfrac{\text{Sum of money}}{\text{Number of persons}}\]
Now, let us find the average of nine persons spent money as
\[\begin{align}
  & \Rightarrow y=\dfrac{12+12+12+12+12+12+12+12+x}{9} \\
 & \Rightarrow y=\dfrac{96+x}{9} \\
\end{align}\]
We are given that the money spent by a ninth person is Rs. 8 more than the average of nine persons.
In mathematical equation this statement can be written as
\[\Rightarrow x=y+8\]
Now, by substituting the value of \['y'\] we got in above equation we get
\[\begin{align}
  & \Rightarrow x=\dfrac{96+x}{9}+8 \\
 & \Rightarrow 9x=96+x+72 \\
 & \Rightarrow 8x=168 \\
 & \Rightarrow x=21 \\
\end{align}\]
So, the amount spent by the ninth person is Rs. 21.
But we are asked to find the total amount spent by 9 persons.
So, by adding the amount spent by each person we get
\[\begin{align}
  & \Rightarrow T=12+12+12+12+12+12+12+12+21 \\
 & \Rightarrow T=117 \\
\end{align}\]
Therefore, the total amount spent by the nine persons is Rs. 117. So, option (d) is the correct answer.

Note: Students may make mistakes in taking the condition.
We are given that the money spent by a ninth person is Rs. 8 more than the average of nine persons.
In the mathematical equation, this statement can be written as
\[\Rightarrow x=y+8\]
But, students will consider as
\[\Rightarrow x=y\times 8\]
This will be wrong because we are given that there is Rs. 8 more not 8 times more. Due to this difference, there may be confusion. Reading questions is important.