The average age of the 9 people in a reading circle does not change when one of them, Kavita, leaves. The eight who remain have a combined age of 296 years. How old is Kavita?

Removing one person leaves the average untouched only if that person was sitting exactly at the average. The eight who remain average 296/8 = 37 years, and that is unchanged from before, so Kavita must be 37. (Check: 296 + 37 = 333 and 333/9 = 37.) 33 divides 296 by 9, the count before she left, but 296 is the total of only the eight who stayed. 35 would make the nine total 331 and average 36.8, so the average would have risen when she left, not held. 39 would make the nine total 335 and average 37.2, so the average would have fallen.