Question

The present age of Aradhana and Aadrika is in the ratio 3:4. 5 years back, the ratio of their ages was 2:3. What is the present age of Aradhana?

12 years
15 years
20 years
22 years
10 years

Answer 1

Given :-

• The present age of Aradhana and Aadrika is in the ratio 3:4.
• 5 years back, the ratio of their ages was 2:3.

To Prove :-

• present age of Aradhana?

Solution :-

▪︎Let the present age be 'x’

▪︎Then 5 years back will be 'x-5’

From the given present age (ratio) 3:4

We can say,

The present age of Aradhana and Aadrika are 3x and 4x respectively.

The ages of Aradhana and Aadrika 5 years before were (3x-5) and (4x-5).

The ratio of their ages (5years back) is 2:3

$\leadsto \sf{(3x-5)/(4x-5) = 2/3} \\ \\ \leadsto \sf{3(3x-5) = 2 (4x-5)} \\ \\ \leadsto \sf{9x-15=8x-10} \\ \\ \leadsto \sf{9x-8x=15–10} \\ \\ \leadsto \boxed{ \underline{\frak {\green{x=5 }}}}$

Therefore, the present ages of

• $\bf{ \pink{Aradhana =3x=15years}}$
• $\bf{ \pink{Aadrika=4x = 20 years}}$

Answer 2

Answer :

✯ Aradhana is 15 years old &

✯ Aadrika is 20 years old.

Explanation :

We know that,

Aradhana and Aadrika's present ages = 3 : 4

Let,

• Aradhana be '3x'
• Aadrika be '4x'

5 years ago,

• Aradhana and Aadrika would be ( x - 5 )

(3x - 5) : (4x - 5)

Solving,

⟶ (3x - 5) / (4x - 5) = 2 / 3

⟶ 3 (3x - 5) = 2 (4x - 5)

⟶ 9x - 15 = 8x - 10

⟶ 9x - 8x = 15 - 10

⟶ x = 5

Substituting 'x' value :

• Aradhana = 3x = 3 × 5 = 15 years
• Aadrika = 4x = 4 × 5 = 20 years