| A train covers a distance in 1 h 40 min, if it runs at a speed of 96 km/h on an average. Find the speed at which the train must run to reduce the time of journey to 1 h 20 min. |
A) 120 km/ h
B) 90 km/h
C) 144 km/h
D) 150 km/h
E) None of these
Correct Answer: E
Solution :
| Here, the person covers \[\frac{1}{2}\]of his journey at \[40\,\,km/h,\]\[\frac{1}{3}\]at\[60\,\,km/h\]and rest \[\left( 1-\frac{1}{2}-\frac{1}{3}=\frac{1}{6} \right)\]at \[30\,\,km/h.\] |
| \[\therefore \]Average speed for whole journey |
| \[=\frac{1}{\frac{1}{2\times 40}+\frac{1}{3\times 60}+\frac{1}{6\times 30}}=\frac{1}{\frac{1}{80}+\frac{1}{180}+\frac{1}{180}}\] |
| \[=\frac{720}{9+4+4}=\frac{720}{17}=42.35\,\,km/h\] |
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