Question

The ages of Ravi Rani are in the ratio of 3:5. After 9 years, the ratio of their ages will become 3:4. The present age of Rani is​

Answer 1

Step-by-step explanation:

Let Ravi's age = 3x or Rani's age = 5x

3x+95x+9=34

⇒4(3x+9)=3(5x+9)

⇒x=3

Rani's age = 5x=5×3=15

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Answer 2

Answer:

The present age of Rani is 15 years.

Step-by-step explanation:

Given:

Ratio of ages of Ravi and Rani = 3 : 5

Ratio of ages of Ravi and Rani after 9 years = 3 : 4

Find:

Present age of Rani = ?

Solution:

Step 1:

Let the age of Ravi = $x$

Let the age of Rani = $y$

Ratio of ages of Ravi and Rani = $x:y = 3:5$

$x:y=3:5$

⇒ $\frac{x}{y} = \frac{3}{5}$  

⇒ $5x=3y$

⇒ $5x - 3y =0$    ---------> eqn. (1)

Step 2:

Age of Ravi after 9 years = $x+9$

Age of Rani after 9 years = $y+9$

Ratio of ages of Ravi and Rani after 9 years =

$x+9:y+9 = 3:4$

⇒ $\frac{x+9}{y+9} = \frac{3}{4}$

⇒ $4(x+9) = 3(y+9)$

⇒ $4x+36 = 3y +27$

⇒ $4x-3y=27-36$

⇒ $4x-3y=-9$     ----------> eqn. (2)

Step 3:

Now, subtract eqn. (2) from eqn. (1),

(1) - (2)

⇒ $5x - 3y =0 \ (-)$

   $4x-3y=-9$

⇒ $x + 0 =9$

⇒ $x=9$

That is, the age of Ravi = 9 years

Step 4:

Substitute $x=9$ in eqn. (1),

⇒ $5x-3y=0$

⇒ $(5 \times 9) -3y =0$

⇒ $45-3y=0$

⇒ $3y=45$

⇒ $y=\frac{45}{3}$

⇒ $y=15$

Therefore, age of Rani = 15 years

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