Question

Ram: If you give 20 rupees to me, I will have twice as much as you.
Sam: If you give me 20 rupees, I will have as much as you have. Total sum of money possessed by them is distributed equally to 30 people. Amount each gets is:
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7
H. 8
I. 9

Answer 1

Hint: For solving this question you should know about making equations for the given statements and to solve that equation. In this problem the statements are given to us and we will make the equations by considering that as a variable term and then we solve that equation for finding the correct answer.

Complete step-by-step solution:
According to our question, Ram: If you give 20 rupees to me, I will have twice as much as you.
Sam: If you give me 20 rupees, I will have as much as you have. Total sum of money possessed by them is distributed equally to 30 people. Amount each gets is:
So, for solving this, we will use the statements.
Let Sam has total rupees as x and Ram has total available rupees as y.
So, according to the given statements,
$\begin{align}
  & \Rightarrow 2\left( x-20 \right)=y+20 \\
 & \Rightarrow 2x-40=y+20 \\
 & \Rightarrow -y+2x=60\ldots \ldots \ldots \left( i \right) \\
\end{align}$
Now the next statement:
$\begin{align}
  & y-20=x+20 \\
 & \Rightarrow y-x=40\ldots \ldots \ldots \left( ii \right) \\
\end{align}$
If we solve both the equations, then,
$\begin{align}
  & 2x-y=60 \\
 & \underline{-x+y=40} \\
 & \text{ }x=100 \\
\end{align}$
And $y=140$
Now we have to distribute the total sum of money to 30 people equally so we divide the total sum $x+Y$ by 30. So we get,
Now: $\dfrac{x+y}{30}=\dfrac{100+140}{30}=\dfrac{240}{30}=8$
So, the answer is 8 and the correct option is H.

Note: While solving this type of questions you should be careful about the statements and equations. This means that you are making the equations from the statement, so ensure that the equations are correct otherwise if that is wrong then your solution for that question will be also wrong.