RRB Group D 17-Sep-2018 Shift 1 Solved Paper

Question : 59 of 100

Marks: +1, -0

It takes hours for a boat to reach its destination and return to its initial place, if the river has no flow. For the same journey it requires 16 hours if the river is flowing. The difference between speeds of boat and river is

15 {km} \/ {hr}

. Find the speed of the flow of the river.

$4 {km} \/ {hr}$
$5 {km} \/ {hr}$
$6 {km} \/ {hr}$
$10 {km} \/ {hr}$

Validate

Solution:

Let

x

and

y

be the speed of river and boat respectively and

D

be the distance.
Then

{ATQ}, 2 {D}=15 ×( {y}- {x})

2 {D}=15 × y\{x=0\}\;\;\;\;\;⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(i)

and

16=\;{D}/{x+y}+\;{D}/{y-x}\;\;\;\;\;⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(ii)

Also

y-x=15\;\;\;\;\;⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(iii)

(given)
Solving eqn's (1),(2) and (3)
we get

y^{2}-32 y+240=0

⇒ \;\; (y-20)(y-12)=0

⇒ \;\; y=12,20

From eqn

(3) \;y ≥ 15 ∴ y=20

⇒ \;\; x=20-15=5 {\text "km/hr"}

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