Question : The average age of 5 children in a family is 15 years. The average age of children together with their father and mother is 25 years. If the father is older than the mother by 4 years, then find the age of the mother (in years).
Option 1: 46
Option 2: 48
Option 3: 52
Option 4: 44
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Correct Answer: 48
Solution :
Let the age of the mother be $M$ years.
We know that the average age of the 5 children is 15 years.
Therefore, the sum of the ages of the 5 children is (15 × 5) = 75 years.
Also, the average age of the children together with their father and mother is 25 years.
Since there are 5 children, the total number of people in the family is 5 + 2 (father and mother) = 7.
Using the formula for the average, we can write the equation:
$\frac{(75 + M + F)}{7} = 25$ ..........(i)
where F represents the age of the father.
We are also given that the father is older than the mother by 4 years:
$F = M + 4$
Substituting F = M + 4 in equation(i) :
$\frac{(75 + M + M + 4)}{7} = 25$
⇒ $2M + 79 = 175$
⇒ $2M = 96$
⇒ $M = 48$
Therefore, the age of the mother is 48 years.
Hence, the correct answer is 48 years.
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