Question : Ram starts from point A at 8 a.m. and reaches point B at 2 p.m. on the same day. On the same day, Raju starts from point B at 8 a.m. and reaches point A at 6 p.m. on the same day. Both points A and B are separated by only a straight line track. At what time do they both meet?
Option 1: 11:45 a.m.
Option 2: 9:42 a.m
Option 3: 10:42 a.m.
Option 4: 12:42 p.m.
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Correct Answer: 11:45 a.m.
Solution : Let the distance be D Time taken by Ram is 6 hrs and that by Raju is 10 hrs. So, speed of Ram = $\frac{D}{6}$ and speed of Raju = $\frac{D}{10}$ Now, the relative speed = $\frac{D}{6} + \frac{D}{10}=\frac{5D + 3D}{30}=\frac{8D}{30}$ Required time = $\frac{D}{\frac{8D}{30}}=\frac{30}{8}$ hr = 225 min = 3 hr 45 min So, they will meet at (8 a.m. + 3 hr 45 min) min = 11:45 a.m. Hence, the correct answer is 11.45 am.
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