Correct Option: C

Method 1
Let us assume the number be 3p , 3(p+1) and 3(p+2)
According to question,
3p + 3(p+1) + 3(p+2) = 72
⇒ 3p + 3p + 3 +3p + 6 = 72
⇒ 9p +9 = 72
⇒ 9p = 72 - 9
⇒ 9p = 63
⇒ p = 63/9 = 7
∴ Largest number = 3(p + 2)
Put the value of p in above equation.
⇒ Largest number = 3 x ( 7 + 2 )
⇒ Largest number = 3 x 9
⇒ Largest number = 27

Method 2
Let us assume the numbers P , P + 3 ,P+ 6
According to Question,
sum of three numbers = 72
P + P + 3 + P + 6 = 72
⇒ 3P + 9 = 72
⇒ 3P = 72 - 9
⇒ 3P = 72 - 9
⇒ P = 63/3
⇒ P = 21
So largest Number = P + 6 = 21 + 6 = 27