Sush was thrice as old as Poonam 6 years back. Sush will be `(5)/(3)` times as old as Poonam 6 years hence. How old is Poonam today ?

Options

A. 20
B. 14
C. 12
D. 15

Explanation

To solve the problem step by step, let's denote Poonam's age 6 years ago as \( x \).

### Step 1: Define the ages
- Poonam's age 6 years ago = \( x \)
- Sush's age 6 years ago = \( 3x \) (since Sush was thrice as old as Poonam)

### Step 2: Express present ages
- Present age of Poonam = \( x + 6 \)
- Present age of Sush = \( 3x + 6 \)

### Step 3: Set up the equation for the future ages
In 6 years, their ages will be:
- Poonam's age in 6 years = \( (x + 6) + 6 = x + 12 \)
- Sush's age in 6 years = \( (3x + 6) + 6 = 3x + 12 \)

According to the problem, Sush's age in 6 years will be \( \frac{5}{3} \) times Poonam's age in 6 years. Therefore, we can set up the equation:
\[ 3x + 12 = \frac{5}{3}(x + 12) \]

### Step 4: Clear the fraction
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 3(3x + 12) = 5(x + 12) \]
This simplifies to:
\[ 9x + 36 = 5x + 60 \]

### Step 5: Solve for \( x \)
Now, rearranging the equation gives:
\[ 9x - 5x = 60 - 36 \]
\[ 4x = 24 \]
\[ x = 6 \]

### Step 6: Find Poonam's current age
Since \( x \) represents Poonam's age 6 years ago, we can find her current age:
\[ \text{Poonam's current age} = x + 6 = 6 + 6 = 12 \]

Thus, Poonam is **12 years old today**.

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