A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $$6\frac{1}{2}$$ hours. The speed of the current is?
A. 1 km/hr
B. 2 km/hr
C. 1.5 km/hr
D. 2.5 km/hr
Answer: Option B
Solution(By Examveda Team)
let speed of boat in still water = x km/hSpeed of stream current = y km/h
According to question,
$$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{x + y}} = 6h\,......\,(i) \cr & \frac{{36}}{{x - y}} + \frac{{24}}{{x + y}} = \frac{{13}}{2}h\,......\,(ii) \cr} $$
In these type of questions, make factor of 24 and 36 and choose the common values which satisfy the above equations.
$$\eqalign{ & {\text{24 = 2,3,4,6,8,}}\boxed{12} \cr & 36 = 3,4,9,\boxed{12} \cr} $$
Choose the common factor i.e. Put this value in equation (i)
$$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{12}} = 6 \cr & \frac{{24}}{{x - y}} + 3 = 6 \cr & x - y = 8 \cr & \therefore x + y = 12 \cr & \therefore x = 10\,\,\,,\,\,\,\,y = 2 \cr & {\text{Speed of the current,}} \cr & y = 2{\text{ km/h}} \cr} $$
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Comments ( 2 )
Related Questions on Boats and Streams
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. None of these
A. 8.5 km/hr
B. 9 km/hr
C. 10 km/hr
D. 12.5 km/hr
E. None of these
A. 2 : 1
B. 3 : 2
C. 8 : 3
D. Cannot be determined
E. None of these
A. 4 km/hr
B. 5 km/hr
C. 6 km/hr
D. 10 km/hr
let upstream= a
downstream= b
24 /a + 36/b= 6 ............. (i)
36/a+24/b= 13/2 ...........(ii)
equation (i) * 3 - equation (ii) *2
after solving this we will get b=12
insert the value of b in equation (i);
we will get a= 8
(a+b)/2 = still water speed of boat
=> 10
so, speed of the current is = 2 (answer)
What is common factor,
I cant understood, can you explain it?