# Ramu wants to go back to his village from Delhi where he works. He uses cab for the same. The cab runs at the rate of 180 kmph and reaches his village

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Ramu wants to go back to his village from Delhi where he works. He uses cab for the same. The cab runs at the rate of 180 kmph and reaches his village 20 minutes early of schedule. On returning back to Delhi, same cab runs at an average speed of 120 kmph, it reaches 30 minutes late. What is distance between his village and Delhi.
1. 500 km
2. 300 km
3. 200 km
4. 400 km

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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.