A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24

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24 Jun 2016 Time and distance

A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream is 13/2 hours. The velocity of the current (in km/hr) is.

OPtion

1) 1
2) 2
3) 1.5
4) 2.5
5) 3
6) 4
7) 3.5
8) 4.5
9) 5
10)None of these

Solution

Let speed upstream & speed downstream be x km/hr and y km/hr respectively. Then
24/x + 36/y = 6 and 36/x + 24/y = 13/2
=> 24u + 36v = 6 and 36u + 24v = 13/2 (u = 1/x and v = 1/y)
Adding we get
u = 1/8 and v = 1/2
=> x = 8 and y = 12
Velocity of current = 1/2 (12-8) km/hr = 2 km/hr

Option 2)

Correct Option: 2 Best Solution (6)

Mukund Manohar   8 years AGO

Let rate upstream = x km/h and rate downstream = y km/h
Then,(24/x) + (36/y) = 36 ------(i)
and (36/x) + (24/y) = 13/2 -------(ii)
Adding (i) and (ii),
60((1/x) + (1/y)) = 25/2
=> (1/x) + (1/y) = 5/24 -------(iii)
Subtracting (i) from (ii)
12((1/x) - (1/y)) = 1/2
=> (1/x) - (1/y) = 1/24 --------(iv)
Adding (iii) and (iv)
2/x = 6/24
=> x = 8
So (1/8) + (1/y) = 5/24
=> y = 12
Speed Upstream = 8 km/h and
Speed Downstream = 12 km/h
So,Velocity of Current = (1/2) * (12-8)
= 2 km/h

Like? Yes (31) | No (13)  

PRATHIBHA ERROLLA   8 years AGO

using the relation that distance/speed= time.
let u= velocity of upstream and v= velocity of downstream
24/u + 36/v = 6
36/u + 24/v = 13/2
solving the equations, we get u=8km/hr and v=12km/hr
we know, velocity of current is (v-u)/2
hence, velocity of current is 2km/hr

Like? Yes (16) | No (12)  

Tejaswi Paricharla   8 years AGO

boat covers 24km upstream & 36 km downstream in 6 hrs==>
6=24/(v1-v2)+36/(v1+v2) where v1=boat velocity,v2=current velocity
boat covers 36 upstream and 24 downstream in 13/2 hrs==>
6.5=36/(v1-v2)+24/(v1+v2)
by solving 2 eqn's we get v2=2km/hr

Like? Yes (4) | No (1)  

Kumar Navendu   8 years AGO

let upstream velocity be x
and downstream velocity be y

so,

24/x + 36/y = 6-----------1
36/x + 24/y = 13/2---------2
dividing eq 1 by eq 2

x/y = 2/3

put y = 3x/2 in eq 1

hence x=8 and y = 12

so velocity of current = (12-8)/2=2

Like? Yes (7) | No (10)  

sudiptaa   8 years AGO

24/(vb-vs)+36/(vb+vs)=6
36/(vb-vs)+24/(vb-vs)=6.5
vs=2

Like? Yes (4) | No (7)  

RAVAL   8 years AGO

Let rate upstream = x km/h and rate downstream = y km/h
so that 24/x + 36/y = 36 ....(1)
and 36/x + 24/y = 13/2....(2)
by solving above 2 equation,
we got x = 8 km/h and y = 12 km/h
now, rate of current = 0.5 (12 - 8) = 2 km/h

Like? Yes (3) | No (10)