Question

- Mahesh's father is 4 times as
old as Mahesh. After 8 years the
ratio of their ages becomes 5:2
find their present ages.​

Answer 1

Let Mahesh's age be x years,

Father's age = 4x

After 8 years,

Mahesh's age = x+8

Father's age = 4x+8

According to the question,

= (4x+8)/(x+8) = 5/2

= 2(4x+8) = 5(x+8)

= 8x+16 = 5x+40

= 3x = 24

= x = 8 years

Father's age = 4x = (8*4) years = 32 years.

Hence, Mahesh's age is 8 years and his father's age is 32 years.

I hope this helps.

Answer 2

Concept Used :-

Formulation of Linear Equation from Word Problem

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem in to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

$\huge\underline{\sf{Solution-}}$

Let

• Mahesh present age be 'x' years.

So,

• Mahesh Father's present age be '4x' years.

After 8 years,

• Mahesh age will be ( x + 8 ) years

and

• Mahesh Father's age will br ( 4x + 8 ) years.

According to statement,

Ratio of Mahesh Father's age and Mahesh age = 5 : 2

$\rm :\longmapsto\:\dfrac{4x + 8}{x + 8} = \dfrac{5}{2}$

$\rm :\longmapsto\:8x + 16 = 5x + 40$

$\rm :\longmapsto\:8x - 5x = 40 - 16$

$\rm :\longmapsto\:3x = 24$

$\rm :\implies\:x = 8$

Hence,

• Present age of Mahesh = 8 yeara

and

• Present age of Mahesh Father's = 32 years