Speed of Jatin and Nitin, who are 60 km apart, is (a + 5) km/h and (a - 5) km/h respectively. If both of them move towards each other, then they will meet after (6a + 30) minutes. Which of the following statement(s) is/are true?
I. Distance covered by Jatin before meeting Nitin is 40 km.
II. (a + 5)² = 25a
III. Time taken by Nitin to reach the initial position of Jatin is 6 hours.

Solution

Relative speed of Jatin w.r.t Nitin = a + 5 + a - 5 = 2a km/h ATQ; 2a X (6a + 30) ÷ 60 = 60 Or, 2a X (6a + 30) = 3600 Or, 12a² + 60a = 3600 Or, a² + 5a - 300 = 0 Or, a² + 20a - 15a - 300 = 0 Or, a(a + 20) - 15(a + 20) = 0 Or, (a + 20) (a - 15) = 0 So, 'a' = 15 or 'a' = -20 But 'a' cannot be negative. So, 'a' = 15 Statement I: Speed of Jatin = 15 + 5 = 20 km/h Time taken for meeting = 6 X 15 + 30 = 120 minutes Required distance = 20 X (120/60) = 40 km So, statement I is true. Statement II: (15 + 5)² = 20² = 400 25 X 15 = 375 So, statement II is NOT true. Statement III: Speed of Nitin = 15 - 5 = 10 km/h Required time = 60/10 = 6 hours So, statement III is true. Therefore, statements I and III are true.