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 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)(y−2)=xy

Therefore, xy−2x+10y−20=xy

⇒−2x+10y−20=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.

(x−10)(y+3)=xy

Therefore, xy+3x−10y−30=xy

⇒3x−10y−30=0

⇒3x−10y=30 ———- (2)

⇒x=50 km/h

Using this in (2), we get

150−10y=30

⇒y=12

Therefore, the distance is 50×12=600 km