Out of five numbers A,B,C,D and E, the average of the first four numbers A,B,C and D is greater than the average of the last four numbers B.C,D and E by 35. Find the difference between A and E.

Options

A. A)80
B. B)120
C. C)130
D. D)140

Answer

To solve the problem, we need to find the difference between the numbers A and E based on the information given about their averages. Let's break it down step by step.

### Step 1: Write down the averages
We know that the average of the first four numbers A, B, C, and D is given by:

\[ \text{Average of } A, B, C, D = \frac{A + B + C + D}{4} \]

Similarly, the average of the last four numbers B, C, D, and E is:

\[ \text{Average of } B, C, D, E = \frac{B + C + D + E}{4} \]

### Step 2: Set up the equation based on the problem statement
According to the problem, the average of the first four numbers is greater than the average of the last four numbers by 35. Therefore, we can write:

\[ \frac{A + B + C + D}{4} - \frac{B + C + D + E}{4} = 35 \]

### Step 3: Simplify the equation
To eliminate the fractions, we can multiply the entire equation by 4:

\[ (A + B + C + D) - (B + C + D + E) = 140 \]

### Step 4: Cancel out common terms
Now, we can simplify the left side of the equation:

\[ A + B + C + D - B - C - D - E = 140 \]

This simplifies to:

\[ A - E = 140 \]

### Step 5: Conclusion
Thus, the difference between A and E is:

\[ \text{Difference } (A - E) = 140 \]

### Final Answer
The difference between A and E is **140**.

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