Question

In a cricket match five batsmen $A,B,C,D,E$ scored an average of 36 runs. D scored 5 more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored $107$ between them. How many runs did E score?
A. 62
B. 45
C. 28
D. 20

Answer 1

Hint: We start solving this question by assuming E’s score to be $x$. Now, we form an equation by using the information that D scored more than E; E scored 8 fewer than A; B scored as many as D and E combined; and B and C scored $107$ between them. Now we add scores of five batsmen and divide it by $5$ and equate the equation to $36$ and solve to get the desired answer.

Complete step-by-step answer:
We have been given that in a cricket match five batsmen $A,B,C,D,E$ scored an average of 36 runs.
We have to find the runs E score.
Let us assume E’s score to be $x$.
As we have been given D scored 5 more than E,
So, we have D’s score $=x+5$.
Now, we have been given that B scored as many as D and E combined, So we have
B’s score $=x+5+x$
Now, we have been given that E scored 8 fewer than A or we can say that A scored 8 more than E,
So, we have A’s score $=x+8$
Now, also given in the question that B and C scored $107$ between them so, we have
$B+C\text{ }\!\!'\!\!\text{ s score = 107}$
Or can write
 $\begin{align}
  & x+5+x+C\text{ }\!\!'\!\!\text{ s score = 107} \\
 & \Rightarrow \text{5+2x+}C\text{ }\!\!'\!\!\text{ s score = 107} \\
 & \Rightarrow C\text{ }\!\!'\!\!\text{ s score}=107-5-2x \\
 & \Rightarrow C\text{ }\!\!'\!\!\text{ s score}=102-2x \\
\end{align}$
Now, given in the question average score of all five batsmen is 36 runs.
So, the total scores will be $\left( A+B+C+D+E \right)'s\text{ score}$.
Substituting the values, we get
$\begin{align}
  & x+8+5+2x+102-2x+x+5+x \\
 & =3x+120 \\
\end{align}$
Now, we know that $\text{Average=}\dfrac{\text{Sum}}{\text{Total number of batsmen}}$
Now, substituting the values, we get
$36=\dfrac{3x+120}{5}$
Now, solving further we have
$\begin{align}
  & 36\times 5=3x+120 \\
 & 180=3x+120 \\
 & 180-120=3x \\
 & 60=3x \\
 & x=\dfrac{60}{3} \\
 & x=20 \\
\end{align}$
We have E’s score as $20$.
Option D is the correct answer.

Note: The possibility of mistake in this question is that students may equate the sum to $36$, which gives a wrong answer. Also, be careful while forming the equations. Read the information given in the question carefully and one by one form the equation.