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# A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. Q.3

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How i solve this optional chapter question, of exercise 3.7 in easiest way . I think it is also an important type of question. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

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1. ## Let the speed of the train be x km/h and the time has taken be y h. The total distance is then xy km. Case1: Speed increases by 10 km/h and the time taken reduces by 2 hours.

The distance traveled remains xy km.
(x+10)(y2)=xy
Therefore, xy2x+10y20=xy
2x+10y20=0
2x+10y=20 ———- (1)
Case 2:
Speed decreases by 10 km/h, then the time taken increases by 3 hours.
However, the distance remains,xy km.
(x10)(y+3)=xy
Therefore, xy+3x10y30=xy
3x10y30=0
3x10y=30 ———- (2)
x=50 km/h
Using this in (2), we get
15010y=30
y=12
Therefore, the distance is 50×12=600 km

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