Question

Math :-
1. Five years ago, the average age of six members of a family was 30. Now a child is included in the family. So the sum of ages of all the family members becomes 22 times the age of the child. The age of the child is equal to :- Correct answer is 10 years.
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Answer 1

Question :-

Five years ago, the average age of six members of a family was 30. Now a child is included in the family. So the sum of ages of all the family members becomes 22 times the age of the child. The age of the child is equal to :-

Given :-

• 5 years ago, the average of 6 members = 30
• 5 years hence, a child is included
• The sum of the ages of all the 7 family members becomes 22 times the age of the child.

To find :-

• The age of the child.

Let the family member's ages before 5 years be :- x, y, z, a, b, c, respectively.

According to the question,

$\dfrac{x + y + z + a + b + c}{6} = 30$

Hence,

$x + y + z + a + b + c = 30 \times 6 = > 180$

After 5 years, their ages will be :-

• x + 5
• y + 5
• z + 5
• a + 5
• b + 5
• c + 5

The sum of ages now will be :-

$= > x + 5 + y + 5 + z + 5 + a + 5 + b + 5 + c + 5$

$= > x + y + z + a + b + c + 5 + 5 + 5 + 5 + 5 + 5$

As we already know the value of x + y + z + a + b + c, Substituting it,

$180 + 30 = > 210$

Let the child's age be d

According to the question,

$210 + d = 22(d)$

$= \geqslant 210 = 22d - d$

$= \geqslant 210 = 21d$

Transposing 21 to the LHS (Left Hand side),

$\dfrac{210}{21} = d$

$10 = d$

Therefore the child's age is :-

10 years.