Question

Of the three numbers second is twice the first and is also thrice the third if the average of the three numbers is 44 the largest number will be​

Answer 1

Answer :-

Largest number is second number i.e 72.

Explanation :-

Let the second number be x

Second number = twice the first number(f)

⇒ x = 2f

⇒ x/2 = f

⇒ f = x/2

i.e First number = x/2

Also Second number = thrice the third number(t)

⇒ x = 3t

⇒ x/3 = t

⇒ t = x/3

i.e Third number = x/3

Given

Average of the three numbers = 44

$\sf \implies \dfrac{sum \ of \ numbers}{number \ numbers} = 44 \\ \\ \\ \sf \implies \dfrac{x + \frac{x}{2} + \frac{x}{3} }{3} = 44 \\ \\ \\ \sf \implies x + \dfrac{x}{2} + \dfrac{x}{3} = 44 \times 3 \\ \\ \\ \sf \implies x + \dfrac{x}{2} + \dfrac{x}{3} = 132 \\ \\ \\ \tt \underline{taking \ lcm} \\ \\ \\ \sf \implies \dfrac{6x + 3x + 2x}{6} = 132 \\ \\ \\ \sf \implies \dfrac{11x}{6} = 132 \\ \\ \\ \sf \implies 11x = 132 \times 6 \\ \\ \\ \sf \implies 11x = 792 \\ \\ \\ \sf \implies x = \dfrac{792}{11} \\ \\ \\ \sf \implies x = 72$

i.e Second number = x = 72

First number = x/2 = 72/2 = 36

Third number = x/3 = 72/3 = 24

Therefore the largest number is second number i.e 72.