#### 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.

#### Solution

Let Viru's present age be x years.

Sudhir's present age = (5 + 3x) years

Anil's present age = `((5 + 3"x")/2)` years

∴ From the given information,

`(5 + 3"x") + ("x") : 3(5 + 3"x")/2 = 5 : 6`

⇒ `(5 + 4x)/(3(5 + 3"x")/2` = `5/6`

⇒ `(2(5 + 4"x"))/(15 + 9x) = 5/6`

⇒ `(10 + 8"x")/(15 + 9"x") = 5/6`

⇒ 6 (10 + 8x) = 5 *(15 + 9x)

⇒ 60 + 48x = 75 + 45x

⇒ 48x - 45x = 75 - 60

⇒ 3x = 15

⇒ x = 5

Hence, Viru's age is 5 years.

Is there an error in this question or solution?

Solution Sudhir'S Present Age is 5 More than Three Times the Age of Viru. Anil'S Age is Half the Age of Sudhir. Concept: Word Problems of Equation in One Variable.