The correct option is A (Speed of boat =8 km/h & Speed of stream =3 km/hr)
Let the speed of boat in still water=x km/hr and
The speed of stream=y km/hr
Speed of boat at downstream,
⇒(x+y)km/hr
Speed of boat at upstream,
⇒(x−y)km/hr
∵time=distancespeed
Time taken to cover 30 km upstream ⇒30x−y
Time taken to cover 44 km downstream⇒44x+y
According to the first condition,
⇒30x−y=44x+y=10
Time taken to cover 40 km upstream ⇒40x−y
Time taken to cover 55 km downstream ⇒55x+y
According to the second condition,
⇒40x−y=55x+y=13
Let 1x−y=uand1x+y=v
⇒30u+44v=10.....eq1
⇒40u+55v=13.....eq2
Multiplying eq1 by 5 and eq2 by 4 and subtract both
⇒(150u+220v=50)−(160u+220v=52)
⇒−10u=−2⇒u=15
put u=15 in eq1
⇒30×15+44v=10⇒44v=4⇒v=111
⇒u=1x−y=15⇒x−y=5...eq3
⇒v=1x+y=111⇒x+y=11...eq4
Adding eq3 and eq4, we get
⇒x−y+x+y=5+11
⇒2x=16
∴x=8
Put x=8 in eq3
⇒8−y=5
⇒y=8−5
∴y=3
Hence, the speed of the boat in still water=8 km/hr
The speed of stream=3 km/hr