CAT 2017 Slot 2 — QA Question 6

Let the average height of 22 toddlers be ‘x’ inches.

Now as the average height of the 2 toddlers who leave the group is one-third the average height of the entire group 22, their average = x/3 inches.

Further, the average height of the balance 20 toddlers in terms of x will be ‘x + 2’ inches. So the average height of all 22 toddlers can be expressed as

x = $\frac{2\left({\displaystyle \frac{x}{3}}\right)+20(x+2)}{22}$

Hence, 22x = 2x/3 + 20x + 40

⇒ x = 30

So the average height of the balance

20 toddlers will be 30 + 2 or 32 inches.

Hence, option (c).