The distance between Rahul's house and the gym is 60 km.

Solution

ATQ, For statement-I: Usual time taken to reach his Gym = (60/25) = (12/5) hours Time taken to reach gym when travelling at 20 km/h = (12/5) + (15/60) = (159/60) hours So, distance travelled by the Rahul when travelling at 20 km/h = 20 × (159/60) = 53 km Therefore, the data given in statement-I is false. For statement-II: Usual time to reach his gym = (60/160) = (3/8) hours Time taken to reach gym by travelling at 96 km/h = (3/8) + (15/60) = (3/8) + (1/4) = (5/8) hours So, distance travelled by the Rahul when travelling at 96 km/h = 96 X (5/8) = 60 km = 60 km Therefore, data given in statement-II is true. For statement-III: Usual time to reach his gym = (60/30) = 2 hours Time taken to reach the gym by travelling at (80/3) km/h = 2 + (15/60) = 2 + (1/4) = (9/4) hours So, distance travelled by the Rahul when travelling at (80/3) km/h = (80/3) × (9/4) = 60 km So, data given in statement-III is true. Therefore, Only II and III are true.