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The average age of a group of six children is 15 years. From the group, two children left, whose ages were 3 years more and 5 years more than the average age. 4 new children, whose average age is 4 years more than the given average age, join the group. Find the new average age.
  • a)
    15 years 
  • b)
    16 years 
  • c)
    17 years 
  • d)
    18 years 
  • e)
    12 years
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The average age of a group of six children is 15 years. From the group...
Sum of the ages of 6 children = 15 × 6 = 90
When two children left, sum of the ages of 4 children = 90 − (18 + 20) = 52
Sum of the ages of new children = (15 + 4) × 4 = 76
∴ Required average = 76 + 52 /8 = 128 /8 = 16 years
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Most Upvoted Answer
The average age of a group of six children is 15 years. From the group...
Let's break down the problem step by step to find the new average age after the changes.

Given:
- The average age of a group of six children is 15 years.

Step 1: Calculate the sum of the ages of the six children.
Since the average age is given as 15 years, we can multiply the average by the number of children to find the sum of their ages.
Sum of ages = Average age * Number of children
Sum of ages = 15 * 6
Sum of ages = 90

Step 2: Subtract the ages of the two children who left.
The ages of the two children who left are given as 3 years more and 5 years more than the average age.
So, the ages of the two children are 15 + 3 = 18 years and 15 + 5 = 20 years.
Subtracting these ages from the sum of ages calculated in Step 1:
New sum of ages = Sum of ages - (Age of child 1 + Age of child 2)
New sum of ages = 90 - (18 + 20)
New sum of ages = 90 - 38
New sum of ages = 52

Step 3: Add the ages of the four new children.
The average age of the four new children is given as 4 years more than the given average age of 15 years.
So, the average age of the four new children is 15 + 4 = 19 years.
To find the sum of their ages, we can multiply the average age by the number of children.
Sum of ages of new children = Average age of new children * Number of new children
Sum of ages of new children = 19 * 4
Sum of ages of new children = 76

Step 4: Calculate the new total sum of ages.
New total sum of ages = New sum of ages + Sum of ages of new children
New total sum of ages = 52 + 76
New total sum of ages = 128

Step 5: Calculate the new average age.
New average age = New total sum of ages / Total number of children
New average age = 128 / (6 - 2 + 4)
New average age = 128 / 8
New average age = 16

Therefore, the new average age of the group after the changes is 16 years (option B).
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