Sanjay and Sonia start from a given point and travel by car on a straight road at an average speed of 30 km and 50 km per hour respectively. Sanjay starts at 10 am and Sonia starts 3 hours later. Find the time when Sonia meets Sanjay.

Sanjay and Sonia start from a given point and travel by car on a straight road at an average speed of 30 km and 50 km per hour respectively. Sanjay starts at 10 am and Sonia starts 3 hours later. Find the time when Sonia meets Sanjay.

1. A
5:30 p.m
2. B
7:30 p.m
3. C
2:30 p.m
4. D
4:30 p.m

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Solution:

It is given the average speeds of 30 km and 50 km per hour of Sanjay and Sonia respectively.
Let the time taken for which Sanjay to cover a distance be x hours.
Sonia starts 3 hours later than Sanjay.
Time taken for Sonia to drive a car to cover a distance will be ‘x – 3’ hours
Given that the two cars start from the same point and they will meet again when they have covered equal distances.
Distance covered by Sonia = Distance covered by Sonia
30x = 50(x – 3)
30x = 50x – 150
20x = 150
x = 7.5
i.e, time taken by Sanjay to cover the distance is 7 hours and 30 minutes
Thus, the time when Sonia meets Sanjay will be at 10:00 hours + 7:30 hours = 17:30 hours or 5:30 p.m
Hence, the required time is 5:30 p.m.
Therefore, 1 is the correct option.

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