Question

Present ages of Shalu and Ritu are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find their present ages.​

Answer 1

Required Answer :

Present age of Ritu = 40 years

Present age of Shalu = 32 years

Given :

• Ratio of the present age of Shalu and Ritu = 4 : 5
• Ratio of their ages after 8 years = 5 : 6

To find :

• The present age of Shalu and Ritu

Solution :

Let,

• Present age of Shalu = 4x
• Present age of Ritu = 5x

Their ages after 8 years :

• Age of Shalu = 4x + 8
• Age of Ritu = 5x + 8

According to the question,

⇒ (4x + 8)/(5x + 8) = 5/6

⇒ 6(4x + 8) = 5(5x + 8)

⇒ 24x + 48 = 25x + 40

⇒ 24x - 25x = 40 - 48

⇒ - x = - 8

⇒ x = 8

The value of x = 8

⇒ Present age of Shalu = 4x

⇒ Present age of Shalu = 4(8)

⇒ Present age of Shalu = 32 years

⇒ Present age of Ritu = 5x

⇒ Present age of Ritu = 5(8)

⇒ Present age of Ritu = 40 years

Answer 2

Given:

➜Ratio of the present age of Shalu and ritu→ 4:5

➜Ratio of their ages after 8 years→ 5:6

Find To:

➜Present Age Of Shalu and Ritu= ?

Solution:

➜Let Present Age of Shalu And Ritu be 4x years and 5x years respectively.

After 8 years,

➨Shalu age = (4x + 8) years

➨Ritu age = (5x + 8) years

$\tt \therefore \: the \: ratio \: of \: their \: ages \: after \: 8 \: years \: = \frac{4x + 8}{5x + 8}$

This is given to be 5:6

$\therefore \tt \: \frac{4x + 8}{5x + 8} = \frac{5}{6}$

➨Cross Multiplication Gives,

➜6(4x + 8) = 5(5x + 8)

➜OR 24x + 48 = 25x + 40

➜OR 24x + 48 - 40= 25x

➜OR 24x + 8= 25x

➜OR 8= 25x - 24x

➜OR 8= x

➨Therefore,

${ \red{ \fbox{\sf{shalu \: present \: age → 4x = 4 × 8 = 32 \: years }}}}$

${ \red{ \fbox{ \sf{Ritu \: present \: age → \: 5x = 5×8 = 40 \: years}}}}$