Three numbers are in the ratio $\frac{3}{4}:\frac{5}{8}:\frac{7}{12}$. If the difference between the greatest and the smallest number is 48, then the value of the greatest number will be:

216

Here,

$\frac{3}{4}:\frac{5}{8}:\frac{7}{12}$

⇒ Taking LCM 24,

⇒ 6 x 3 : 3 x 5 : 2 x 7

⇒ 18 : 15 : 14

⇒ The difference between the greatest and the smallest number = 48

⇒ (18 - 14)units = 48

⇒ 12 units = 48

⇒ 1 unit = 12,

⇒ The greatest number = 18 x 12 = 216.