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Question

# A train, after travelling 70 km from a station A towards a station B, develops a fault in the engine at C and covers the remaining journey to B at 34 of its earlier speed and arrives at B 1 hour and 20 minutes late. If the fault had developed 35 km further on at D, it would have arrived 20 minutes sooner. Find the speed (in km / hr) of the train.

A
30
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B
45
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C
60
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D
15
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Solution

## The correct option is C 45Let, the train's speed = y∴ Total time =10+xyCase I :Total time =70y+x34y=70y+4x3y=210+4x3y∴210+4x3y=70+xy+1+13⇒210+4x3y=210+3x+3y+y3y⇒210+4x=210+3x+4y⇒x−4y=0 ......... (i)Case II : Total time =70+35y+x−3534y=70+35y+4x−1403y=105×3+4x−1403y=315−140+4x3y=175+4x3y∴175+4x3y=70+xy+1⇒175+4x3y=70+x+yy⇒175+4x=210+3x+3y⇒4x−3x=210−175⇒x−3y=45 ............. (ii)We have,(i) ⇒x−4y=0(i) ⇒x−3y=45x−4y=0x−3y=0____________−y=−45 ⇒y=45 km/h∴ Speed of train = 45 km/h

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