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Rajdhani express starts from Delhi at 7 : 00 AM with speed 105 km/hr and reaches Lucknow and stops there for 45 minutes. While returning from Lucknow it decreases its speed by 20% and reaches Delhi at 5 : 12 PM on the same day, then what is the distance between Delhi and Lucknow? 

Rajdhani express starts from Delhi at 7 : 00 AM with speed 105 km/hr and reaches Lucknow and stops there for 45 minutes. While returning from Lucknow it decreases its speed by 20% and reaches Delhi at 5 : 12 PM on the same day, then what is the distance between Delhi and Lucknow?  Correct Answer 441 km

Given:

Speed of Rajdhani express while going to Lucknow = 105 km/hr

Speed of Rajdhani while returning = 80% of 105 km/hr

Rajdhani Express stops at Lucknow station for 45 minutes

Formula Used:

Distance = Speed × Time

Calculation:

Let the distance between Delhi and Lucknow = D

Total time of the journey including stoppage time at Lucknow = 10 hours 12 minutes

Total time of the journey excluding stoppage time at Lucknow = 9 hours 27 minutes = 9.45 hours

Decreased speed = 80% of 105 = 84 km/h

According to the question :

⇒ (D/105) + (D/84) = 9.45

⇒ (4D + 5D)/420 = 9.45

⇒ 9D = 9.45 × 420

⇒ D = 441 km

∴ The distance between Delhi and Lucknow is 441 km.

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