Question
The distance between Rahul's house and the gym is 60 km.
When travelling at ___ km/h, Rahul reaches the gym at his usual time. However, when he reduces his speed to ___ km/h, he arrives 15 minutes late. The values given in which of the following options will fill the blanks in the same order to make the statement true? I. 25 and 20 II. 160 and 96 III. 30 and (80/3)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.
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