In a cricket match five batsman A, B, C, D and 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 ?

Options

A. 62
B. 45
C. 28
D. 20

Answer

To find out how many runs E scored, we can break down the problem step by step.

### Step 1: Calculate the total runs scored by all batsmen.
The average score of the five batsmen A, B, C, D, and E is 36 runs. Therefore, the total runs scored by all five batsmen can be calculated as follows:

\[ \text{Total runs} = \text{Average} \times \text{Number of batsmen} = 36 \times 5 = 180 \]

**Hint:** Remember that the total runs can be found by multiplying the average score by the number of players.

### Step 2: Define the scores of the batsmen in terms of E's score.
Let E's score be \( x \).

- Since D scored 5 more than E:
\[ D = x + 5 \]

- E scored 8 fewer than A:
\[ A = x + 8 \]

- B scored as many as D and E combined:
\[ B = D + E = (x + 5) + x = 2x + 5 \]

- B and C scored 107 runs between them:
\[ B + C = 107 \implies C = 107 - B = 107 - (2x + 5) = 102 - 2x \]

**Hint:** When defining variables, express each player's score in relation to E's score.

### Step 3: Set up the equation for total runs.
Now, we can express the total runs scored by all batsmen in terms of \( x \):

\[ A + B + C + D + E = 180 \]

Substituting the expressions we found:

\[ (x + 8) + (2x + 5) + (102 - 2x) + (x + 5) + x = 180 \]

### Step 4: Simplify the equation.
Combining like terms:

\[ x + 8 + 2x + 5 + 102 - 2x + x + 5 + x = 180 \]

This simplifies to:

\[ (1x + 2x - 2x + 1x + 1x) + (8 + 5 + 102 + 5) = 180 \]

\[ 3x + 120 = 180 \]

### Step 5: Solve for \( x \).
Subtract 120 from both sides:

\[ 3x = 180 - 120 \]
\[ 3x = 60 \]

Now, divide by 3:

\[ x = 20 \]

### Conclusion: Find E's score.
Thus, E's score is:

\[ \text{E's score} = x = 20 \]

**Final Answer:** E scored 20 runs.

---