Question : Three numbers are such that the average of the first two numbers is 2, the average of the last two numbers is 3 and the average of the first and the last numbers is 4. What is the average of the three numbers?
Option 1: 2
Option 2: 3.5
Option 3: 3
Option 4: 2.5
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Correct Answer: 3
Solution :
Let the numbers in order be a, b, and c.
According to the question,
a + b = 2 × 2 = 4-----------(i)
b + c = 2 × 3 = 6-----------(ii)
c + a = 2 × 4 = 8-----------(iii)
On adding (i), (ii), and (iii), we get,
2 (a + b + c) = 4 + 6 + 8 = 18
$\therefore$ a + b + c = $\frac{18}{2}$ = 9
So, the required average = $\frac{9}{3}$ = 3
Hence, the correct answer is 3.
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