Three numbers are in the ratio $\frac{1}{4} : \frac{5}{9} : \frac{7}{12}.$The difference between the greatest and the smallest number is 180, Find the sum of all the three numbers.

750

Here,

\(\frac{1}{4}\) : \(\frac{5}{9}\) : \(\frac{7}{12}\)

⇒ Taking LCM as 36,

⇒ 9 : 20 : 21

⇒ Difference between the greatest and the smallest number = 180

⇒ 21 - 9 = 12 units = 180

⇒ 1 unit = 15.

⇒ Sum of all the three numbers = (9 + 20 + 21) x 15 = 50 x 15 = 750.