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Question

A train with a speed of $$90$$ km/hr crosses a bridge in $$36$$ seconds. Another train $$100$$ metres shorter crosses the same bridge at $$45$$ km/hr. What is the time taken by the second train to cross the bridge?


A
18 seconds
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B
52 seconds
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C
64 seconds
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D
72 seconds
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Solution

The correct option is D $$64$$ seconds
Let the length of the bridge be $$x$$ metres and length of the first train at $$90$$ km/hr be $$y$$ metres 
Then $$\displaystyle (x+y)=\left [ \left ( 90\times \frac{5}{18} \right )\times 36 \right ]$$ m $$=900$$ m
The second train crosses the bridge by covering  distance of $$[x + (y - 100)] m$$ at the rate of $$45$$ km/hr
$$12.5$$ m/s i.e. $$800$$ m at $$12.5$$ m/s $$\displaystyle (\because x+y=900 \ \text{m})$$
Time taken by the second train to cross the bridge $$\displaystyle =\frac{800}{12.5}$$ sec $$=64$$ seconds

Mathematics

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