A train leaves Delhi at 10 a.m. and reaches Jaipur at 4 p.m. on same day. Another train leaves Jaipur at 12 p.m. and reaches Delhi at 5 p.m. on same day. What is the time of day (approximately) when the two trains will meet?

Total time taken by first train = 6 hours and second train = 5 hours

$$\because speed \propto\frac{1}{time}$$

=> Let speed of first train = $$5x$$ km/hr and speed of second train = $$6x$$ km/hr

=> Distance between Delhi and Jaipur = $$5x\times6=30x$$ km

At 10:00 am, first train starts moving, => distance covered by it in 2 (12-10) hours = $$5x\times2=10x$$ km

Distance left between the two trains at 12:00 pm = $$30x-10x=20x$$ km

Now, at 12:00 pm both move towards each other, => relative speed = $$5x+6x=11x$$ km/hr

=> Time taken to meet each other = $$(\frac{20x}{11x}\times60)$$ minutes $$\approx 109$$ minutes

= 1 hour and 49 minutes

$$\therefore$$ Time at which they will meet = 12:00 pm + 1 hour and 49 minutes = 1:49 pm

=> Ans - (D)