Question

Sudhir's present age is 5 more than three times the age of Viru, Anil's age is half the age of Sudhir. If the ratio of the sum of Sudhir's and Viru's age to three times Anil's age is 5: 6, then find Viru's age.

Answer 1

Hint: To find the Viru’s age first of all suppose the present age of Viru is x years. Then find Sudhir's present age in terms of x. Then also find Anil's present age in terms of x. In the last use the given ratio according to the given condition.

Complete step-by-step answer:
Let viru's age \[ = x\] years
So according to the question
⇒ Sudhir's age \[ = 5 + 3x\;\] years
Similarly Anil’s age will be
⇒ Anil's age \[ = \dfrac{{5 + 3x}}{2}\;\] years
In this problem it is mentioned that the ratio of the sum of Sudhir's and Viru's age to three times Anil's age is \[5:\;6\]
So mathematically we can write
  \[\dfrac{{x + 5 + 3x}}{{\dfrac{{3\left( {5 + 3x} \right)}}{2}}} = \dfrac{5}{6}\]
On simplifying we get
 \[ \Rightarrow \dfrac{{2\left( {4x + 5} \right)}}{{5 + 3x}} = \dfrac{5}{2}\]
Or,
 \[ \Rightarrow \left( {8x + 10} \right)2 = 25 + 15x\]
Or,
 \[ \Rightarrow 16x + 20 = 15x + 25\]
Or,
 \[ \Rightarrow x = 5\;\] years.
Hence the present age of Viru is 5 years.
So, the correct answer is “5 years”.

Note: In this problem we can also arrange the person from younger to senior like Viru is smallest, Anil is middle age (10 years) and Sudhir is oldest (20 year) among the three. So if a question is asked who is the oldest then also we can answer.