Question

7.
The ratio of Sakhi's age to Seema's age is 3 : 2. Five years from now, the
ratio of their ages will be 7:5. Find their present ages.
(Ans : 30 years, 20 years)​

Answer 1

Given :

• The ratio of Sakhi's age to Seema's age is 3:2.
• Five years from now, the ratio of their ages will be 7:5.

To Find :

• Present ages of both

Solution :

Let,

• Present age of Sakhi = 3x
• Present age of Seema = 2x

After 5 years,

• Age of Sakhi = 3x + 5
• Age of Seema = 2x + 5

According to the Question :

⠀⟶⠀3x + 5/2x + 5 = 7/5

• Cross multiplication

⠀⟶⠀5(3x + 5) = 7(2x + 5)

⠀⟶⠀15x + 25 = 14x + 35

⠀⟶⠀15x - 14x = 35 - 25

⠀⟶⠀x = 10

Therefore :

• Present age of Sakhi = 3x
• Present age of Sakhi = 3 × 10
• Present age of Sakhi = 30 years

• Present age of Seema = 2x
• Present age of Seema = 2 × 10
• Present age of Seema = 20 years

⛬ Present age of Sakhi and Seema are 30 years and 20 years respectively.

___________________

Answer 2

Given :

• The ratio of Sakhi's age to Seema's age is 3 : 2.

• Five years from now, the ratio of their ages will be 7:5

To Find :

• Present Ages

Solution :

✬ As here in the Question we are given Sakhi and seema Age's are in ratio. So, let the age of Sakhi be 3y and seema be 2y. Five years from now there Ages will be 7 :5. Let the age of Sakhi be 3y+ 5 and seema age be 2y + 5. and then we will find the Present ages.

• Let Sakhi's age be 3y
• Let Seema's age be 2y

After 5 years

• Sakhi's age = 3y + 5
• Seema's age = 2y + 5

A.T.Q

➛ 3y + 5/2y + 5 = 7/5

➛ 5 (3y + 5) = 7 (2y + 5)

➛ 15y + 25 = 14y + 35

➛ 15y - 14y = 35 - 25

➛ y = 10

Now, Present ages :

Sakhi age

• ➛ 3y = 3 × 10
• ➛ 30 Years

____________

Seema's age

• ➛ 2y = 2 × 10
• ➛ 20 years

____________