1.

A train covered a certain distance at a uniform speed. If the train had been 5 kmph faster, it would have taken 3 hours less than the scheduled time. And, if the train were slower by 4 kmph, it would have taken 3 hours more than the scheduled time. Find the length of the journey.

Answer» Correct Answer - 1080 km
Let the original speed of the train be x kmph and let the time taken to complete the journey be y hours.
Then, length of the journey = xy km.
Case I Speed = `( x + 5)` kmph and time taken = ` ( y - 3) ` hours.
` therefore xy = (x + 5) ( y - 3 ) rArr 5y - 3x = 15" "`... (i)
Case II Speed ` = ( x - 4) `kmph and time taken ` = ( y + 3) ` hours
` therefore xy = (x - 4) ( y + 3) rArr 3x - 4y = 12 " " `... (ii)
From (i) and (ii), we get ` x = 40 and y = 27` .
` therefore ` length of the journey = ` x y = 40 xx 27 ` km = 1080 km.


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