Question

The age of a girl in month 9 is equal to the age of her grandmother in years. If the difference between their ages is 66 years, find their ages.
A) The age of a girl is 5 years and that of a grandmother is 60 years.
B) The age of a girl is 6 years and that of a grandmother is 72 years.
C) The age of a girl is 7 years and that of a grandmother is 84 years.
D) The age of a girl is 8 years and that of the grandmother is 96 years.

Answer 1

Hint: In order to solve this type of problems related to age, we need to follow the following steps:-
a.) Express what we don't know as a variable.
b.) Create an equation based on the information provided.
c.) Solve for the unknown variable.
d.) Substitute our answer back into the equation to see if the left side of the equation equals the right side of the equation and hence, we will get our final result.

Complete step by step solution: In this problem, the age of the girl and the grandmother have to be determined. For solving the question, at first, we need to solve the relation about the ages of the girl and her grandmother as per the question.
Let the age of a girl be ‘a’ years and let the age of grandmother be ‘g’ years.
Now, writing the equation for each statement:-
The age of a girl in months is equal to the age of her grandmother in years.
     $\Rightarrow 12a=g$ (i) [ 1 year = 12 months ]
Now, it the difference between their ages is 66 years:-
     $\Rightarrow {g-a}=66$ (ii)
Placing value of $g=12a$ from equation (i) in equation (ii);
$\Rightarrow{g-a}=66$
$\Rightarrow{12a-a}=66$
$\Rightarrow 11a=\ 66$
$\Rightarrow a=\dfrac{66}{11}=6$
$\therefore \ \ a=6$

Putting value of a in equation (i);
$\Rightarrow 12a=g$
$\Rightarrow g=12\times 6$
$\Rightarrow g=72$
$\therefore $ age of the girl $=a=6$ years.
age of the grandmother $\Rightarrow{g}=72$ years.

Therefore, option (B) is the correct answer to this question.

Note: In order to solve age-related problems, we need no some of the important points which are as follows:-
a.) If the present age is y, then n times the present age = ny.
b.) If the present age is x, then age n years later/hence = x + n.
c.) If the present age is x, then age n years ago = x – n.
d.) The ages in a ratio a: b will be ax and bx.