Correct Answer: 18

Solution : Given,
Average of 24 observations = 41
⇒ Sum of 24 observations = 41 $\times$ 24 = 984
Also, The average of the first 9 observations is 42.
⇒ Sum of first 9 observations = 42 $\times$ 9 = 378 ......(1)
And, The average of the last 16 observations is 39.
⇒ Sum of last 16 observations = 39 $\times$ 16 = 624 ........(2)
Adding (1) and (2), we get,
⇒ Sum of first 9 observations + Sum of last 16 observations = Sum of 24 observations + 9th observation
As 9th observation is counted twice in the first 9 and last 16 observations.
⇒ 378 + 624 = 984 + 9th observation
$\therefore$ 9th observation = 18
Hence, the correct answer is 18.