Question

If the average of \(a\) and \(b\) is 70, and the average of \(b\) and \(c\) is 110, what is the value of \(c - a\)?

• A. \(90\)
• B. \(40\)
• C. \(150\)
• D. \(80\)
• E.

Hint:

When solving average-based questions, always convert the average equation into a sum equation. Subtracting or adding such equations often simplifies the problem.

Answer 1

The Correct Option is A

Step 1: Write the average conditions.
\[ \frac{a+b}{2} = 70 \quad \Rightarrow \quad a+b = 140 \quad \cdots (1) \] \[ \frac{b+c}{2} = 110 \quad \Rightarrow \quad b+c = 220 \quad \cdots (2) \] Step 2: Subtract the equations.
From (2) – (1): \[ (b+c) - (a+b) = 220 - 140 \quad \Rightarrow \quad c - a = 80 \] Step 3: Compare with options.
The correct value of \(c - a\) is \(80\).
Final Answer: \[ \boxed{80} \]