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02 May 2025, 00:30
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D
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A boat takes 4 hours more upstream while going x km than downstream in a river if it travels with a speed 2 times the speed of river. How much more time (in minutes) will be taken to travel upstream than downstream in a river while going 2x km if it travels 5 times the speed of the river?
A. 30
B. 40
C. 50
D. 60
E. 70
A. 30
B. 40
C. 50
D. 60
E. 70
02 May 2025, 02:48
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Bunuel
Let speed of Boat = b
Speed f stream = s
Time = Distance / Speed
Downstream speed = b+s
Upstream speed = b-s
Downstream time = x/b+s
Upstream time = x/b-s
\(\frac{x}{b+s} +4 = \frac{x}{b-s}\)
b = 2s (given)
i.e. \(\frac{x}{3s} +4 = \frac{x}{s}\)
i.e. \(\frac{2x}{3s} = 4\)
i.e. \(\frac{x}{s} = 6\)
How much more time (in minutes) will be taken to travel upstream than downstream in a river while going 2x km if it travels 5 times the speed of the river?
\(\frac{2x}{b-s} - \frac{2x}{b+s} =\) ???
where b = 5s
I.e. \(\frac{2x}{4s} - \frac{2x}{6s} = \frac{x}{2s} - \frac{x}{3s} = \frac{x}{6s} = 6/6 =1\)
i.e. 60 minutes
Answer: Option D
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02 May 2025, 18:16
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A boat takes 4 hours more upstream while going x km than downstream in a river if it travels with a speed 2 times the speed of river. How much more time (in minutes) will be taken to travel upstream than downstream in a river while going 2x km if it travels 5 times the speed of the river?
.......Distance..........Speed...........Time
U..... x km ...........(2s-1s) ............. t (Upstream= speed of boat -speed of river)
D..... x km ...........(2s+1s) ............. (t-4) hrs (Downstream=speed of boat + speed of river)
Distance is same so, (1s)t=(3s)(t-4) ; t=6 hrs
Hence, x=(1s)(t)=6s
.......Distance..........Speed...........Time
U..... 2x km ...........(5s-1s) .............
D..... 2x km ...........(5s+1s) .............
x=6s; Upstream Time=D/S= 2x/(4s)= 12s/4s=3 hrs
Also, Downstream Time=2x/6s=12s/6s =2 hrs
Difference between time taken while going upstream and downstream= 3-2=1 hr= 60 minutes
Answer: D
.......Distance..........Speed...........Time
U..... x km ...........(2s-1s) ............. t (Upstream= speed of boat -speed of river)
D..... x km ...........(2s+1s) ............. (t-4) hrs (Downstream=speed of boat + speed of river)
Distance is same so, (1s)t=(3s)(t-4) ; t=6 hrs
Hence, x=(1s)(t)=6s
.......Distance..........Speed...........Time
U..... 2x km ...........(5s-1s) .............
D..... 2x km ...........(5s+1s) .............
x=6s; Upstream Time=D/S= 2x/(4s)= 12s/4s=3 hrs
Also, Downstream Time=2x/6s=12s/6s =2 hrs
Difference between time taken while going upstream and downstream= 3-2=1 hr= 60 minutes
Answer: D
