Multiple choice

Two cyclists Ajay and Sunil are at a distance of 120 km from each other.Both starts at same time speed of Ajay is 12 km/hr while speed of Sunil increases by 1 km/hr every hr with speed being 10 km/hr starting in the first hour , in how many hours will both cyclist meets ?

  1. 3 hrs

  2. 4 hrs

  3. 5 hrs

  4. 8 hrs

  5. 10 hrs
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ajay distance = 12t. Sunil distance = 10 + 11 + 12 + 13 + 14... (sum of arithmetic progression). Total distance = 120. 12t + (t/2)(20 + (t-1)1) = 120. 12t + 10t + 0.5t^2 - 0.5t = 120. 0.5t^2 + 21.5t - 120 = 0. t^2 + 43t - 240 = 0. (t+48)(t-5) = 0. t = 5.

AI explanation

Using the relative speed concept, the total distance of 120 km is covered by their combined speeds hour by hour. In the first hour they cover 22 km (12 + 10), in the second 23 km (12 + 11), in the third 24 km, in the fourth 25 km, and in the fifth 26 km, totaling 120 km. Therefore, they will meet in 5 hours.

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