The ratio of lengths of two trains is 5 : 3 and the ratio of their speeds is 6 : 5. The ratio of time taken by them to cross a pole is ?
A. 5 : 6
B. 11 : 8
C. 25 : 18
D. 27 : 16
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{A}}\,{\text{:}}\,{\text{B}}\,\,\,\,\,\,\,{\text{length}} \cr & {\text{Ratio of A's and }} \to 5:3\,\,\,\left( {5x:3x} \right) \cr & {\text{ B's length}} \cr & {\text{Ratio of A's and }} \to 6:5\,\,\,\left( {6y:5y} \right) \cr & {\text{ B's speed}} \cr} $$We know that,
When a train crosses a pole, i.e., it covers the distance equal to its length
Time taken by train A to cross the pole :
$$ = \frac{{{\text{Total distance}}}}{{{\text{Speed}}}} = \frac{{5x}}{{6y}}$$
Time taken by train B to cross the pole :
$$ = \frac{{{\text{Total distance}}}}{{{\text{Speed}}}} = \frac{{3x}}{{5y}}$$
Ratio of the their time :
$$\eqalign{ & = {\text{A}}:{\text{B}} \cr & = \frac{{5x}}{{6y}}:\frac{{3x}}{{5y}} \cr & = 25:18 \cr} $$
Related Questions on Speed Time and Distance
A. 48 min.
B. 60 min.
C. 42 min.
D. 62 min.
E. 66 min.
A. 262.4 km
B. 260 km
C. 283.33 km
D. 275 km
E. None of these
A. 4 hours
B. 4 hours 30 min.
C. 4 hours 45 min.
D. 5 hours
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