Question

A is 2 years older than B who is twice as old as C. If the total of the ages of A, B and C be 27 years, then how old is B?
A. 7 years
B. 8 years
C. 9 years
D. 10 years

Answer 1

Hint: Here first assume the age of C in terms of any variable and then find the age of A and B respectively as per the conditions given in the question.

Complete Answer:
Let the age of C be ‘x’ then according to question, age of B will be twice of age of C,
So, B’s age will be 2x
And it is also given that A is 2 years older than B
So, Age of A is (2 + 2x) years.
It is given that the sum of their ages is 27
Therefore,
\[
  Age{\text{ }}of{\text{ }}A{\text{ }} + {\text{ }}Age{\text{ }}of{\text{ }}B{\text{ }} + {\text{ }}Age{\text{ }}of{\text{ }}C{\text{ }} = {\text{ }}27 \\
   \Rightarrow \left( {{\text{ }}2{\text{ }} + {\text{ }}2x{\text{ }}} \right) + {\text{ }}2x{\text{ }} + {\text{ }}x{\text{ }} = {\text{ }}27 \\
   \Rightarrow 2{\text{ }} + {\text{ }}2x{\text{ }} + {\text{ }}2x{\text{ }} + {\text{ }}x{\text{ }} = {\text{ }}27 \\
   \Rightarrow 5x{\text{ }} + {\text{ }}2{\text{ }} = {\text{ }}27 \\
   \Rightarrow 5x{\text{ }} = {\text{ }}27{\text{ }}-{\text{ }}2 \\
   \Rightarrow 5x{\text{ }} = {\text{ }}25 \\
   \Rightarrow x = \dfrac{{25}}{5} \\
   \Rightarrow x = 5 \\
\]
So, age of A will be 2x +2
Age of A will be
$2 \times 5 + 2\, = 12\,yrs.$
As given,
 age of B is two times age of C
\[\begin{array}{*{20}{l}}
  {Age{\text{ }}of{\text{ }}B{\text{ }} = {\text{ }}2x} \\
  { = {\text{ }}2{\text{ }} \times {\text{ }}5} \\
  { = {\text{ }}10}
\end{array}\]

Hence, option (D) is correct.

Note: In such types of questions first assume the age of any person in terms of any variable and with the assumed age derived age of the other persons and then add all ages and equate to the total given age.