Ananyaa travels a certain distance at a speed of 3 kmph and reaches her destination late by 15 minutes. If she travels at a speed of 4 kmph, she reaches her destination 15 minutes earlier. Find the distance that Ananyaa is traveling to reach her destination.

6 km

The correct answer is Option (4) → 6 km

Let the distance be d km.

Time taken at 3 kmph:

$\frac{d}{3} \text{ hours}$

Time taken at 4 kmph:

$\frac{d}{4} \text{ hours}$

Difference in time = 15 + 15 = 30 minutes = $\frac{1}{2}$​ hour

So,

$\frac{d}{3} - \frac{d}{4} = \frac{1}{2}$

$\frac{4d - 3d}{12} = \frac{1}{2} \Rightarrow \frac{d}{12} = \frac{1}{2} \Rightarrow d = 6$