Question

Ishika and her grandfather both had birthdays last week. The sum of their ages is 100 years. Her grandfather's age is 4 times Ishika's age. How old is Ishika?
(a). 16 years
(b). 20 years
(c). 22 years
(d). 25 years

Answer 1

Hint: For solving this question, we assume the age of Ishika to be ‘x’ years. As given in the question, her grandfather's age is 4 times of Ishika’s age. By using this given condition, we can easily calculate the age of her grandfather in terms of x. The sum of their ages is a hundred years. Using this condition, we easily evaluate the age of Ishika

Complete step-by-step solution -

Let the age of Ishika be ‘x’ in years.
 As per given in the question, the age of her grandfather is four times Ishika's present age.
So, the age of her grandfather would be ‘4x’ in years.
It is given that the sum of their ages is 100 years.
\[\begin{array}{*{35}{l}}
   x\text{ }+\text{ }4x\text{ }=\text{ }100 \\
   \Rightarrow 5x\text{ }=\text{ }100 \\
   ~\Rightarrow x=20 \\
\end{array}\]
The age of grandfather is 4x $=4\times 20=80$years.
Hence, the age of Ishika is 20 years.
Therefore, option (b) is correct.

Note: The key concept involved in solving this problem is the interpretation of the problem statement into suitable equations to evaluate the variable. This problem could alternatively be solved by letting the age of grandfather as x and then forming suitable equations for both ages.