The ratio of three numbers is $\frac{1}{4}: \frac{5}{6}: \frac{1}{3}$ respectively. If the sum of the number is 68, what is the value of $\frac{1}{3}$ of the first number?

4

Here,

\(\frac{1}{4}\) : \(\frac{5}{6}\) : \(\frac{1}{3}\)

⇒ Take LCM 12,

⇒ 3 x 1 : 2 x 5 : 4 x 1 = 3 : 10 : 4

⇒ (3 + 10 + 4) units = 68

⇒ 17 units = 68

⇒ 1 unit = 4,

⇒ $\frac{1}{3}$ of 1st number 3 = 3 x 4 = 12 x $\frac{1}{3}$ = 4.