The ratio of the current ages of Rahul and Samir is 3 : 4. T years ago, the ratio of their ages was 2 : 3. The sum of their ages after T years will be 72 years. Find the present age of Samir.

The correct answer is 32 years.

Step-by-step explanation:

Let the present ages of Rahul and Samir be $3x$ years and $4x$ years, respectively.

Step 1: Express their ages T years ago.
T years ago, Rahul's age was $(3x-T)$ years and Samir's age was $(4x-T)$ years.
The ratio of their ages T years ago was 2 : 3.

$\frac{3x-T}{4x-T}=\frac{2}{3}$

Cross-multiplying to simplify:

$3(3x-T)=2(4x-T)$

$9x-3T=8x-2T$

$9x-8x=3T-2T$

$x=T$

Step 2: Express the sum of their ages after T years.
After T years, Rahul's age will be $(3x+T)$ years and Samir's age will be $(4x+T)$ years.
Given that the sum of their ages after T years is 72 years:

$(3x+T)+(4x+T)=72$

Since $T=x$, substitute $T$ with $x$:

$(3x+x)+(4x+x)=72$

$4x+5x=72$

$9x=72$

$x=\frac{72}{9}=8$

Step 3: Calculate Samir's present age.
Samir's present age $=4x=4\times 8=32$ years.

Therefore, the present age of Samir is 32 years.