Sum of three fraction is 2 11/ 24 . If the greatest fraction is divided by the smallest fraction the result is 7/6, which is greater than the middle fraction by 1/3. Find all the three fractions.

Let the greatest, middle and smallest fraction be P, Q and R respectively in decreasing order.
According to the question.
(Greatest fraction) / (Smallest fraction) = 7/6
⇒ P/R = 7/6
⇒ P = 7R/6 ....(i)
and Q = 7/6 - 1/3 = 7 - 2/6 = 5/6 (ii)
Now, P + Q + R = 2¹¹/₂₄ (iii )
Substitute the value of P and Q from Eqs. (i), (ii) and put in Eqs (iii), we get
⇒ 7R/6 + 5/6 + R = 59/24
⇒ (7R + 5 + 6R)/6 = 59/24
⇒ (13R + 5) / 6 = 59/24
⇒ 13R = (59/4) - 5 = 39/4
⇒ R = 39 / (4 x 13)
∴ R = 3/4
On putting the value of R in Eq. (i), we get
P = 7R/6 = (7/6) x (3/4) = 7/8