navodya vidyalaya Exam Numerical Ability Boats and Streams

A BOAT COVER 32 KM UPSTREAM AND 36 KM DOWNSTREAM IN 7 HOURS .ALSO ,IT COVERS 40 KM UPSTREAM AND 48 KM DOWNSTREAM IN 9 HOURS .THE RATIO OF SPEED OF BOAT IN STILL WATER AND SPEED OF THE STREAM IS ?

Read Solution (Total 1)

Speed of boat=10 km/h and stream=2 kmph

Let the speed(in km/h) of boat in still water=x and stream=y, then
1st condition: 32/(x-y) + 36/(x+y) = 7 ---(i) and
2nd condition: 40/(x-y) + 48/(x+y) = 9 ---(ii)
Substituting 1/(x-y) =a and 1/(x+y)=b in above equation, (i) & (ii) becomes
32a + 36b =7 ---(iii) and
40a + 48b= 9 ---(iv)
On solving (iii) & (iv), a=1/8 and b=1/12
=> x-y=8 and x+y=12, so x=10, y=2
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