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.