Correct Answer - Option 2 : 35
Given:
Total number of children is 18.
Average height of these two toddlers is one-fourth the average height of the original 18.
Formula Used:
Average = Sum of observation/Total number of observation
Calculation:
Let the sum of 18 children be a
⇒ Average = a/18
Let the sum of 2 children be x
⇒ Average = x/2
According to the condition,
⇒ x/2 = 1/4(a/18)
⇒ x = 1/2(a/18)
⇒ x = a/36 ----(I)
Also,
⇒ (a – x)/16 = a/18 + 3
⇒ (a – x)/16 = (a + 54)/18
⇒ (a – x)/8 = (a + 54)/9
⇒ 9(a – x) = 8(a + 54)
⇒ 9a – 9x = 8a + 432
⇒ a – 9x = 432
Using the equation I,
⇒ a – 9(a/36) = 432
⇒ a – a/4 = 432
⇒ 3a/4 = 432
⇒ a = (432 × 4)/3
⇒ a = 576
Putting the above value in equation I,
⇒ x = 576/36
⇒ x = 16
Sum of remaining 16 children is,
⇒ 576 – 16
⇒ 560
Average of 16 children is,
⇒ 560/16
⇒ 35
∴ Average height of remaining 16 children is 35.