Question

The average height of 18 children increases by 3 inches when two of them leave this group. If the average height of these two toddlers is one-fourth the average height of the original 18, then the average height, in inches, of the remaining 16 children is
1. 30
2. 35
3. 40
4. 45

Answer 1

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.