When Raghav travels at 15Kmph, he reaches office at 10 AM. If he travels at…
2023
When Raghav travels at 15Kmph, he reaches office at 10 AM. If he travels at 10Kmph, he reaches his office at 10:30 AM. At what speed should he travel so that he reaches his office at 10:15 AM? (Assume he leaves home at same time and takes the same route).
- A.
12
- B.
13
- C.
18
- D.
19
Attempted by 11 students.
Show answer & explanation
Correct answer: A
Answer: 12 km/h
Reasoning:
Let D be the distance (in km). Time at 15 km/h = D/15 hours; time at 10 km/h = D/10 hours. The difference in arrival times is 0.5 hour (30 minutes).
Set up the equation: D/10 - D/15 = 0.5. Factor D: D(1/10 - 1/15) = 0.5. Since 1/10 - 1/15 = 1/30, we get D/30 = 0.5, so D = 0.5 × 30 = 15 km.
To arrive at 10:15 (15 minutes later than 10:00), the travel time must be 0.25 hours longer than the 15 km/h travel time. At 15 km/h the travel time is D/15 = 15/15 = 1.00 hour, so required travel time = 1.00 + 0.25 = 1.25 hours.
Required speed S = distance / time = 15 / 1.25 = 12 km/h.
Therefore, he should travel at 12 km/h to reach the office at 10:15.