Patna and Ranchi are the two places on the same side of the bank of

Question

Patna and Ranchi are the two places on the same side of the bank of a uniformly flowing river. Ankur takes 1 hour to row from Patna to Ranchi and 5 hours from Ranchi to Patna. Find the ratio of speeds of the boat in the still water to that of the river.

(A) 3 : 2
(B) 5 : 2
(C) 4 : 3
(D) 2 : 1
(E) 5 : 4

(A) 3 : 2
(B) 5 : 2
(C) 4 : 3
(D) 2 : 1
(E) 5 : 4

rocky620 · Answer

Lets assume that:

Distance between Patna and Ranchi = 100 kms
Speed of the boat = x km/hr
Speed of the river = y km/hr

Since, Ankur takes less time, rowing from Patna to Ranchi, the river is flowing from Patna to Ranchi (i.e. Patna - Ranchi is DOWNSTREAM & Ranchi to Patna is UPSTREAM)

Time taken form Patna to Ranchi is 1 hour, =>  \frac{100}{x+y}  = 1 => 100 = x+y....... eq.1

Time taken form Ranchi to Patna is 5 hours, =>  \frac{100}{x-y}  = 5 => 20 = x-y......... eq.2

Solving eq.1 & eq.2, 
x = 60
y = 40

So,  \frac{x}{y}  =  3:2

Option A

Jainam24 · Answer

Method 1:
Let Boat's speed be B and river's speed be R 
Let Distance between Patna and Ranchi be 5km. 
Equating in terms of time 
Downstream: 5/(B+R)=1. 
So B+R=5 
upstream: 5/(B-R)=5
So B-R=1

Solving these 2 equations we get B's speed=3 R's speed=2

So ans is Option A 3:2

Method 2:
Let Boat's speed be B and river's speed be R 
Distance between Patna and Ranchi is constant 
 when distance is constant, the time and speed are inversly proportional

Ratio of Downstream time/Upstream time=1/5
So ratio of Downstream speed/Upstream speed=5/1
i.e. (B+R)/(B-R)=5/1
Backsolve from here 
Only option A will work 
Ans Option A

Abhishek009 · Answer

Let total distance between Patna and Ranchi be 10 Units...

So, Upstream Speed :  1 = \frac{10}{S_u}

Thus,  S_u = 10  {10 = s - c}------------>(I)

So, Downstream Speed :  5 = \frac{10}{S_d}

Thus,  S_d = 2  {2 = s + c}------------>(II)

12 = 2s

Or,  s = 6  ie Speed of Boat &  c = 4  ie Current of Stream
 
=>  6 : 4 = 3 : 2 , Answer must be (A)

Yosemite98 · Answer

the distance from P to R is the same as from R to P and D = V * t

The velocity can be expressed as (x+r) and (x-r) where x is speed of the boat and r speed of the river.

D from P to R = D from R to P -> 1*(x+r) = 5 * (x-r)

to get the ratio of x/r we divide the above equation by r -> x/r + 1 = 5* x/r -5

x/r = 3/2

Patna and Ranchi are the two places on the same side of the bank of

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Patna and Ranchi are the two places on the same side of the bank of

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