Correct Answer - Option 2 : 300 km

**Given****∶**

Speed of cab while going to village = 180 kmph, at this speed he reaches 20 minute early.

Speed of cab while going to Delhi = 120 kmph, at this speed he reaches 30 minute late.

**Formula Used****∶**

Time = Distance / Speed

**Calculation****∶**

Let the distance between Delhi and his village be x km

And, the speed in order to reach on time is y km/hr.

So, time taken to reach on schedule will = x/y hours

According to question,

x / 180 = (x / y) – (1 / 3) ---- (1)

x / 120 = (x / y) + (1 / 2) ---- (2)

subtractequation (1) from (2), we get

⇒ (x / 120) – (x / 180) = (1 / 2) – (-1 / 3)

⇒ (3x – 2x) / 360 = (1 / 2) + (1 / 3)

⇒ x = (5 × 360) / 6

⇒ x = 300 km

**∴ The distance between Delhi and his village is 300 km.**