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Two people A and B are at a distance of ...

Two people A and B are at a distance of 110 km from each other at 10:30 AM. After 30 mins, A starts moving towards B at a speed of 20 km/hr while at 12 PM. B starts moving away from A at a speed of 15 km/hr. At what time (in AM) will they meet on the next day?

A

` 6:00`

B

`8:00`

C

`4:00`

D

` 3:00`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these calculations: ### Step 1: Understand the Initial Conditions - At 10:30 AM, A and B are 110 km apart. - A starts moving towards B at 11:00 AM at a speed of 20 km/hr. - B starts moving away from A at 12:00 PM at a speed of 15 km/hr. ### Step 2: Calculate the Distance Covered by A Before B Starts Moving From 10:30 AM to 11:00 AM, A does not move. At 11:00 AM, A starts moving towards B. ### Step 3: Calculate the Distance Between A and B at 12:00 PM - From 11:00 AM to 12:00 PM, A moves for 1 hour at 20 km/hr. - Distance covered by A in 1 hour = Speed × Time = 20 km/hr × 1 hr = 20 km. - Remaining distance between A and B at 12:00 PM = Initial distance - Distance covered by A = 110 km - 20 km = 90 km. ### Step 4: Calculate the Relative Speed After 12:00 PM - After 12:00 PM, A continues to move towards B at 20 km/hr, while B moves away from A at 15 km/hr. - The relative speed between A and B = Speed of A + Speed of B = 20 km/hr + 15 km/hr = 35 km/hr. ### Step 5: Calculate the Time Taken to Meet After 12:00 PM - Using the formula: Time = Distance / Speed - Distance = 90 km (remaining distance) - Speed = 35 km/hr (relative speed) - Time = 90 km / 35 km/hr = 18/7 hours ≈ 2.57 hours. ### Step 6: Convert Time to Hours and Minutes - 18/7 hours = 2 hours and 34 minutes (since 18 ÷ 7 = 2 remainder 4, which is 4/7 of an hour, or approximately 34 minutes). ### Step 7: Calculate the Meeting Time - 12:00 PM + 2 hours and 34 minutes = 2:34 PM. ### Step 8: Determine the Time on the Next Day Since they meet at 2:34 PM on the same day, to find the time on the next day: - 2:34 PM on the next day = 2:34 PM + 24 hours = 2:34 PM next day. ### Step 9: Convert to AM Time To convert 2:34 PM to AM time: - 2:34 PM is equivalent to 14:34 in 24-hour format. - To find the equivalent AM time, we need to subtract 12 hours. - 14:34 - 12:00 = 2:34 AM. ### Final Answer They will meet at **2:34 AM** on the next day.
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