A train leaves Mumbai for Goa at 3:45 pm and goes at the

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A train leaves Mumbai for Goa at 3:45 pm and goes at the rate of 50 km/h. Another train leaves Goa for Mumbai at 2:35 pm and distance between Mumbai and Goa is 510 km. at what distance from Mumbai will the two trains meet ?

1. 200 km
2. 150 km
3. 145 km
4. 300 km

Correct Option: A

Let the two trains meet at D km from Mumbai. Then,
3:45 pm + D/50 = 2 : 35 pm + 510 - D/60
⇒ (3:45 pm - 2:35 pm) + (D/50 + D/ 60) = 510/60
⇒ (1¹/₆ h) + D{( 50 + 60 / 50 x 60)} = 17/2
⇒ D(110/3000) = 17/2 - 7/6
⇒ D(110/3000) = (51 - 7)/6 = 44/6
∴ D = (44/6) x (3000/110) = 200 km