Questions & Answers

Question

Answers

A) \[40years\]

B) \[42years\]

C) \[48years\]

D) \[50years\]

Answer
Verified

Given: Average age of a mother and her six children is \[12years\], if mother’s age is excluded then the average of ages will reduce by \[5\text{ }years\].

Let the age of the mother be \[x\text{ }years\].

The average age of a mother and her six children is \[12\].

Hence, sum of age of the mother and her six children is $12\times 7=84$

\[\left[ Average=\dfrac{Sum\text{ }of\text{ }quantity}{number\text{ }of\text{ }quantity} \right]\] here number of quantity 7 and average is 12.

If we reduce the age of mother then, Sum of age of six children = \[84-x\]

Now average of age of six children = \[\dfrac{84-x}{6}\]

Put the values, and simplify -

According to question: \[\begin{align}

&\Rightarrow \,12-5=\dfrac{84-x}{6} \\

& \Rightarrow 7=\dfrac{84-x}{6}\text{ }\!\![\!\!\text{ 6 from denominator goes to the numerator when change from RHS to LHS }\!\!]\!\!\text{ } \\

& \Rightarrow 7\times 6=84-x \\

\end{align}\]

\[\begin{align}

& \Rightarrow 42=84-x \\

& \therefore x=84-42 \\

& \therefore x=42 \\

\end{align}\]

Hence, The age of the mother is $42\ \text{years}$

Therefore, from the given multiple choices,