Of the three numbers, the average of the first and the second is greater than the average of the second and the third by 25. The difference between the first and the third of these three numbers is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50
Both averages contain the second number, so it cancels when the two averages are subtracted, leaving only the first and the third. Let the numbers be \(a\), \(b\) and \(c\):
The first average is 25 more than the second: \(\displaystyle\frac{a+b}{2}-\frac{b+c}{2}=25\)
With \(b\) cancelled: \(\displaystyle\frac{a-c}{2}=25\)
\(a-c=50\)