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A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster than it would have taken 4 hours less than tit scheduled time. And, if the train were slows by 6 km/hr, then the train would have take 6 hours more than the scheduled time. The lengt1 of the journey is `700\ k m` b. `720\ k m` c. `740\ k m` d. `760\ k m`

Text Solution

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Let the original speed of the train be x kmph and let the time taken to complete the journey be y hours.
Length of whole journey = ( xy ) km.
Case I When speed = ` (x + 6) `kmph and time taken = (` y - 4 `) hours .
Length of total journey = ` (x + 6) ( y - 4 ) ` km.
` therefore xy = (x + 6) ( y - 4) rArr xy = xy - 4x + 6y - 24 `
` rArr 4x - 6y = - 24 rArr 2x - 3y = - 12 " " `... (i)
Case II When speed =` (x - 6) ` kmph and time taken `= ( y + 6) ` hours.
Length of total journey `= (x - 6) ( y + 6)` km.
` therefore xy = ( x- 6) ( y + 6) rArr xy = xy + 6 x - 6y - 36`
` rArr 6x - 6y = 36 rArr x - y = 6" " `... (ii)
On multiplying (ii) by 3 and subtracting (i) from the result, we get
` 3x - 2x = 18 + 12 rArr x = 30 `
On putting ` x= 30 ` in (ii), we get ` y = 30 - 6 = 24`
` therefore x = 30 and y = 24`
So, length of journey = ` (x y ) km = ( 30 xx 24) ` km = 720 km
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