The average of 24 numbers is 56. The average of the first 10 numbers is 71.7 and that of the next 11 numbers is 42. The next three numbers (i.e. 22^nd, 23^rd and 24^th) are in the ratio $\frac{1}{2} : \frac{1}{3} : \frac{5}{12}$. What is the average of the 22^nd and 24^th numbers ?

60.5

Sum of 24 numbers = 56 x 24 = 1344

Sum of first 10 numbers = 71.7 x 10 = 717

Sum of next 11 numbers = 42 x 11 = 462

Sum of 22nd, 23rd and 24th = 1344 - 717 - 462 = 165

Ratio of 22nd, 23rd and 24th = \(\frac{1}{2}\) : \(\frac{1}{3}\) : \(\frac{5}{12}\) = \(\frac{12}{2}\) \(\frac{12}{3}\) \(\frac{12 × 5}{12}\) = 6 : 4 : 5

Ratio of 22nd, 23rd and 24th = 6x : 4x : 5x

6x + 4x + 5x = 165

15x = 165

x = 11

22nd number = 6 x 11 = 66

24th number = 5 x 11 = 55

Average of 22nd and 24th number = 60.5