Question

Luqman is 67. His son Rehan is 29. In how many years will Rehan be exactly half
his father’s age

Answer 1

Step 1 : Define x

Given, Luqman is 67 years old and Rehan is 29 years old.

Let the age of Rehan till he becomes half the age of Luqman be x

So, Luqman's age be 67 + x and Rehan's age be 29 + x

Step 2 : Solve for x

According to the question,

29 + x = $\dfrac{1}{2}$(67 + x)

➾ 2(29 + x) = 67 + x

➾ 58 + 2x = 67 + x

➾ 2x - x = 67 - 58

➾ x = 9

∴ 9 years will be required for Rehan to become half the age of Luqman.

Answer 2

Luqman age = 67

Luqman son rehan age = 29  

let him be half the age after p years  

After p years  

Fathers age = 67 + p

Rehan's age = 29 + p

29 + p = $\bf\huge\frac{1}{2}$ × 67 + p  

2 ( 29 + p) = 67 + p

58 + 2p = 67 + p

2p - p = 67 - 58

p = 9 years

$\bf\huge\boxed{\boxed{\bf\huge\:P\:=\:9years}}}$