a boat covers 24 km upstream and 36 downstream in 6hours while..., Problems On Boats & Streams, General Mathematics

Question:A boat covers `24` km upstream and `36` km downstream in `6`hours while it covers `36` km upstream and `24` km downstream in `6 1/2` hours, The velocity of the current is :

A `1 km∕hr` 
B `1.5 km∕hr` 
C `2 km∕hr` 
D `2.5 km∕hr`

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+ AnswerC

+ ExplanationLet rate upstream = x kmph and rate downstream = y kmph

Then`24/x + 36/y = 6 .....(i)`

and`36/x + 24/y = 13/2 ....(ii)`

Adding (i) and (ii),

`60 (1/x + 1/y) = 25/2`

`or 1/x + 1/y = 5/24 ... (iii)`

Subtracting (i) and from (ii)

`12 (1/x - 1/y) = 1/2`

`or 1/x - 1/y = 1/24 .....(iv)`

Adding (iii) and (iv), we get 

`2/x = 6/24 or x = 8.`

`1/8 + 1/y = 5/24 ⇔ 1/y`

`= (5/24 - 1/8) = 1/12`

`⇔ y = 12.

:. Speed upstream = 8 kmph, speed downstream = 12 kmph

:. Rate of the current`= 1/2 (12 - 8) kmph`

`= 2 kmph`

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