| An express train travelled at an average speed of 100 km/h, stopping for 3 min after every 75 km. A local train travelled at a speed of 50 km/h, stopping for 1 min after every 25 km. If the trains began travelling at the same time, then how many kilometres did the local train travel in the time in which the express train travel 600 km? |
A) 400
B) 405
C) 307.25
D) 415.5
E) None of these
Correct Answer: C
Solution :
| Time taken by express train to cover 75 km including stoppage |
| \[=\left( \frac{60}{100}\times 75 \right)\min \,+3\min =48\min \] |
| Time taken by express train to cover 600 km |
| = Time taken by it to cover 525 km |
| + Time taken by it to cover 75 km |
| \[=\left( \frac{48}{75}\times 525 \right)\min \,+\left( \frac{60}{100}\times 75 \right)\min \] |
| \[=(336+45)\min =381\min \] |
| Time taken by local train to cover 25 km including stoppage \[\left( \frac{60}{25}\times 25 \right)\min +1\min =31\min \] |
| In 31 min, distance covered \[=25\,\,km\] |
| In\[(31\times 12)\min ,\]distance covered |
| \[=\left( \frac{25}{31}\times 31\times 12 \right)=300\,\,km\] |
| In last 9 min, distance covered \[=\left( \frac{25}{31}\times 9 \right)=7.25\,\,km\] |
| \[\therefore \]Required total distance \[=300+7.25=307.25\,\,km\] |
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