Question

Ratio of present age of Rahul and Rahim is 4:5. After 5 years the ratio will become 5:6. Find present age​

Answer 1

Answer :-

Given :-

• Ratio of present age of Rahul and Rahim is 4 : 5.

• Ratio of age after 5 years is 5 : 6

To Find :-

• Present age

Solution :-

Let the present age of Rahul be 4x

Rahim's age = 5x

Age after 5 years :-

Rahul's age will be 4x + 5

Rahim's age will be 5x + 5

According to the question :-

After 5 years, ratio of their ages is 5 : 6.

→ 4x + 5 : 5x + 5 = 5 : 6

→ 4x + 5 / 5x + 5 = 5 / 6

→ 6 ( 4x + 5 ) = 5 ( 5x + 5 )

→ 24x + 30 = 25x + 25

→ 25x - 24x = 30 - 25

→ x = 5

• Rahul's age = 4x = 4 × 5 = 20 years
• Rahim's age = 5x = 5 × 5 = 25 years

Present age of Rahul and Rahim are 20 years and 25 years respectively.

Answer 2

Given :

• Ratio of present ages of Rahul and Rahim is 　4 : 5
• After 5 years, the ratio becomes　　5 : 6

To find :

• The present ages of both

Solution :

• Let present ages of Rahul and Rahim, be 4x and 5x respectively
• So, after 5 years, the ratio of their ages will be 5 : 6

$\sf\implies{(4x+5):(5x+5)=5:6}$

$\sf\implies{{\dfrac{4x+5}{5x+5}}={\dfrac{5}{6}}}$

• By cross multiplying, we get :

$\sf{~~~~~~~~~~6(4x+5)=5(5x+5)}$

$\sf\implies{24x+30=25x+25}$

$\sf\implies{24x-25x=25-30}$

$\sf\implies{{\cancel{-}}x={\cancel{-}}5}$

$\sf{~~~~~~\therefore x={\orange{\underline{\boxed{\sf{\pmb{~5~}}}}}}}$

∴ Required answer :

Present ages of :

• Rahul : 4x = 4 × 5 = 20 years
• Rahim : 5x = 5 × 5 = 25 years