An old man and a young man are working together in an office and staying…
2024
An old man and a young man are working together in an office and staying together in a near by apartment. The old man takes 30 minutes and the young 20 minutes to walk from apartment to office. If one day the old man started at 10.00 AM and the young man at 10:05 AM from the apartment to office, when will they meet?
- A.
10:45
- B.
10:30
- C.
10:15
- D.
10:20
Attempted by 592 students.
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Correct answer: C
Answer: 10:15
Key idea: The old man gets a 5-minute head start. Compute speeds and solve for the time after the young man starts when the young man catches up.
Let the distance to the office be x meters. Old man's speed = x/30 m/min, young man's speed = x/20 m/min.
In the first 5 minutes (before the young man starts) the old man covers 5 * (x/30) = x/6 meters.
After the young man starts, let t be the minutes until they meet. Distance covered by the old man then = x/6 + t*(x/30). Distance covered by the young man = t*(x/20). Set them equal:
1/6 + t/30 = t/20 (divide both sides by x)
Multiply both sides by 60: 10 + 2t = 3t, so t = 10 minutes.
Therefore they meet 10 minutes after 10:05, i.e., at 10:15.
Alternate quick method: Take x = 60 units so speeds are 2 units/min (old) and 3 units/min (young). Old covers 10 units in the first 5 minutes, and the young closes the gap at 1 unit/min, so it takes 10 minutes to catch up → meeting at 10:15.