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Rajat beats Nitin by 240 m in a 1560 m race. Then they go to race on a slope where Rajat starts from bottom of the slope and Nitin starts from top of the slope they run towards each other and when they meet Nitin has travelled 20 m more than Rajat. If the speed of any person on the slope, compared to normal speed, becomes (150/11)%  more in decline and 10% less in incline, what was the total length of the slope? 

Rajat beats Nitin by 240 m in a 1560 m race. Then they go to race on a slope where Rajat starts from bottom of the slope and Nitin starts from top of the slope they run towards each other and when they meet Nitin has travelled 20 m more than Rajat. If the speed of any person on the slope, compared to normal speed, becomes (150/11)%  more in decline and 10% less in incline, what was the total length of the slope?  Correct Answer 605 m

Distance travelled by Nitin, when Rajat finishes the race = 1560 – 240 = 1320 m

As we know, the speed is directly proportional to the distance covered if the time taken is constant.

Thus, the ratio of speeds of Rajat and Nitin = 1560/1320 = 13/11

Let 13x and 11x be the speeds of Rajat and Nitin respectively.

On the slope,

New speed of Rajat = (1 – 10%)13x = (0.9)13x = 11.7x

New speed of Nitin = (1 + 3/22)11x = (25/22)11x = 12.5x

Let’s assume Rajat and Nitin met each other on the slope after t time.

Then, according to question, 12.5xt – 11.7xt = 20 ⇒ xt =20/0.8 = 25

Thus, total length of the slope = 12.5xt + 11.7xt = 24.2xt = 24.2 × 25 = 605 m

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