Of the three numbers, the second is twice the first and is also thrice the third. If the average of the three numbers is 44, what is the largest number?

Concept Used:-

The average of the group of numbers is the ratio of the sum of all the numbers given to the total number.

The formula to found the average is given below.

⇒ Average = (sum of all the observation) / (Total number of observation)

Explanation:-

Suppose, that the three numbers are A, B and C.

Since, the second is twice the first and is also thrice the third. Thus,

\(\Rightarrow B=2 A=3 C\)             ......(1)

From equation (1) we get,

\(\Rightarrow A=\frac{B}{2} \text { and } C=\frac{B}{3}\)

Also, given that the average of the three numbers is 44. Thus,

\(\Rightarrow \frac{\mathrm{A}+\mathrm{B}+\mathrm{C}}{3}=44 \\ \Rightarrow \frac{\mathrm{B}}{2}+\mathrm{B}+\frac{\mathrm{B}}{3}=44 \times 3\\ \Rightarrow \frac{3+6+2}{6}B=132 \\ \Rightarrow B=132 \times \frac{6}{11}\\ \Rightarrow B=72 \)

Also,

\(\Rightarrow A = \dfrac{72}{2}=36\\ \Rightarrow C = \dfrac{72}{3}=24\)

So, the largest number is 72.

Hence, the correct option is 3.