Question

If the sum of three consecutive multiples of 9 is 108, then the largest multiple amongst them is ____.

• A. 27
• B. 36
• C. 45
• D. None of the above

Answer 1

The correct option is C 45

If $x$ is a multiple of 9, then next multiple is $x+9$.

The next to this is $x+9+9=x+18$

So, three consecutive multiples of 9 are $x,x+9,x+18$

As per the question,
$x+(x+9)+(x+18)=108$
⇒ $3x+27=108$
⇒ $3x+27=108$
⇒ $x=\frac{108-27}{3}=\frac{81}{3}=27$
So, the largest multiple is 27 + 18 = 45