Option 4 : 6

__Calculation:__

Let the two-digit number be **'ab';**

When expanded, it will be equivalent to **10a + b**;

When reversed, it will be **'ba'** i.e. **10b + a;**

Given, the number is increased by 75%;

We have Percentage increase = \(\rm \dfrac {new \; - \; original}{original} \times 100\)

From the above relation,

\(75 = \dfrac {(10b \; + \; a) - (10a \; + \; b)}{10a \; + \; b} \times 100\)

\(⇒ \dfrac {3}{4} = \dfrac {9b \; - \; 9a}{10a \; + \; b}\)

⇒ 30a + 3b = 36b - 36a

⇒ 66a = 33b ⇒ **2a = b**;

Now, the original number ab will be equivalent to

ab = 10a + b = **12a**;

This indicates it is divisible by 12, which is **divisible by 6** as well.

5, 7 and 11 are not possible as the two-digit number ab ⇒ 0 ≤ a ≤ 9; 0 ≤ b ≤ 9;

But we have 2a = b ⇒ a can only take 1, 2, 3 and 4;

Hence, 12a is divisible by 6 but not by 5, 7 or 11;