The two trains leave Varanasi for Lucknow at 11:00 a.m. and at 11:30 a.m., respectively and travel at a speed of 110 km/h and 140 km/h, respectively. How many kilometers from Varanasi will both trains meet?

Let the train which leaves Varanasi at 11:00 be A and another train be B.

Speed of train A = 110 km/hr

Speed of train B = 140 km/hr

Distance covered by train A in 30 min(30/60 = 1/2 hr) = speed $$\times time = 110 \times 1/2 = 55 km$$

At 11:30, distance between both trains will be 55 km.

Relative speed of train B = 140 - 110 = 30 km/hr

Time taken by train B to meet = 55/30 = 11/6 hr

Distance covered by train B in 11/6 hr = 140 $$\times 11/6 = 256 \frac{2}{3}$$

$$\therefore 256 \frac{2}{3}$$ kilometers from Varanasi will both trains meet.