Question
Train A travelling at 60 km/hr leaves Mumbai for Delhi at 6 pm. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 pm. Train C leaves Delhi for Mumbai at 9 pm. If all the three trains meet at the same time between Mumbai and Delhi, then what is the speed of train C if the distance between Delhi and Mumbai is 1260 km ?
Answer: Option C
Suppose the three trains meet x hours after 9 pm
Let the speed of train C be y km/hr
Distance travelled by train A in (x + 3) hrs = Distance travelled by train B in x hrs
⇒ 60 (x + 3) = 90x
⇒ 30x = 180
⇒ x = 6
⇒ Also, distance travelled by train B in x hrs + distance travelled by train C in x hrs = 1260 km
⇒ 90x + yx = 1260
⇒ 540 + 6y = 1260
⇒ 6y = 720
⇒ y = 120
Hence, speed of train C = 120 km/hr
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Suppose the three trains meet x hours after 9 pm
Let the speed of train C be y km/hr
Distance travelled by train A in (x + 3) hrs = Distance travelled by train B in x hrs
⇒ 60 (x + 3) = 90x
⇒ 30x = 180
⇒ x = 6
⇒ Also, distance travelled by train B in x hrs + distance travelled by train C in x hrs = 1260 km
⇒ 90x + yx = 1260
⇒ 540 + 6y = 1260
⇒ 6y = 720
⇒ y = 120
Hence, speed of train C = 120 km/hr
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