Elementary Boat problem

[Aman verma]

Q: A boat covers 48 km upstream and 72 km downstream in 12 hours , while it covers 72 km upstream and 48 km downstream in 13 hours. The speed of the stream is :

a) 2 km/hr

b) 2.2 km/hr

c) 2.5 km/hr

d) 4 km/hr

e)4.5 km/hr

OA[spoiler]a)[/spoiler]

[brijesh]

Q: A boat covers 48 km upstream and 72 km downstream in 12 hours , while it covers 72 km upstream and 48 km downstream in 13 hours. The speed of the stream is :

First eq.
48/(x-y) + 72/(x+y) = 12
Sec eq.
72/(x-y) + 48/(x+y) = 13

1/(x+y)[72*72- 48*48]= 12*72- 13*48

x+y = [72*72- 48*48]/ [12*72- 13*48]

similarly x-y and then get the value of y (stream speed) and x (boat speed)

Some one have any short method?

[diebeatsthegmat]

Q: A boat covers 48 km upstream and 72 km downstream in 12 hours , while it covers 72 km upstream and 48 km downstream in 13 hours. The speed of the stream is :

a) 2 km/hr

b) 2.2 km/hr

c) 2.5 km/hr

d) 4 km/hr

e)4.5 km/hr

OA[spoiler]a)[/spoiler]

are you sure the answer is A? i think the answer is C

Let x and y be the upstream and downstream speed respectively.
48/x+72/y=12
72/x+48/y=13
solve this we will get y=1.5x or y=15 and x=10
We know that Speed of the stream = 1/2 * (downstream speed - upstream speed)=1/2(15-10)=2.5
the answer is C