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. 22nd, 23rd and 24th) are in the ratio $\frac{1}{2} : \frac{1}{3} : \frac{5}{12}$. What is the average of the 22nd and 24th numbers ?
Answer & explanation
Correct answer: option 1
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