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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# 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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## Let the speed of the train beÂ xÂ km/h and the time has taken beÂ yÂ h.

The total distance is thenÂ xyÂ km.

Case1:

Speed increases byÂ 10Â km/h and the time taken reduces byÂ 2Â hours.

The distance traveled remainsÂ xyÂ km.

(x+10)(yâˆ’2)=xy

Therefore,Â xyâˆ’2x+10yâˆ’20=xy

â‡’âˆ’2x+10yâˆ’20=0

â‡’âˆ’2x+10y=20Â ———- (1)

Case 2:

Speed decreases byÂ 10Â km/h, then the time taken increases byÂ 3Â hours.

However, the distance remains,xyÂ km.

(xâˆ’10)(y+3)=xy

Therefore,Â xy+3xâˆ’10yâˆ’30=xy

â‡’3xâˆ’10yâˆ’30=0

â‡’3xâˆ’10y=30Â ———- (2)

â‡’x=50Â km/h

Using this in (2), we get

150âˆ’10y=30

â‡’y=12

Therefore, the distance isÂ 50Ã—12=600Â km