Sum of three fractions 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 fraction be x, y and z respectively in decreasing order.
Then, according to the question,
x/z = 7/6
⇒ x = 7z/6
And y = 7/6 - 1/3 = 7-2/6 = 5/6
Now, x + y + z = 2¹¹/₂₄
⇒ 7z/6 + 5/6 + z = 59/24
⇒ (13z + 5)/ 6 = 59/24
⇒ 13z = 59/4 - 5 =39/4
⇒ z = 3/4
∴ x =7z/6 = 7/8
Hence, the fraction are 7/8, 5/6, 3/4.