| 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 goes at the rate of 60 km/h. If the distance between Mumbai and Goa is 510 km, at what distance from Mumbai will the two trains meet? |
A) 200 km
B) 150 km
C) 145 km
D) 300 km
Correct Answer: A
Solution :
| Let the two trains meet at x km from Mumbai. |
| Then, \[3:45\,\,pm+\frac{x}{50}=2:35\,\,pm+\frac{510-x}{60}\] |
| \[\Rightarrow \]\[(3:45\,\,pm-2:35\,\,pm)+\left( \frac{x}{50}+\frac{x}{50} \right)=\frac{510}{60}\] |
| \[\Rightarrow \]\[\left( 1\frac{1}{6}h \right)+x\left( \frac{60+50}{50\times 60} \right)=\frac{17}{2}\] |
| \[\Rightarrow \]\[x\,\,\left( \frac{110}{3000} \right)=\frac{17}{2}-\frac{7}{6}\] |
| \[\Rightarrow \]\[x\left( \frac{110}{3000} \right)=\frac{51-7}{6}=\frac{44}{6}\] |
| \[\therefore \]\[x=\frac{44}{6}\times \frac{3000}{110}=200\,\,km\] |
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