SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 43 of 100

Marks: +1, -0

On a river, Q is the mid-point between two points P and R on the same bank of the river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 minutes. How long would it take to go from R to P ?

$3 1/ 3$ hours
5 hours
$6 2/ 3$ hours
$7 1 /3$ hours

Validate

Solution:

(4) Let PQ = QR = z km.
Let speed of boat in still water be x kmph. and speed of current be y kmph.
According to the question,

{z}/{x+y}+ {z}/{x-y}=12... (i)

and

{2 z}/{x-y}=16 {40}/{60}

⇒{2 z}/{x-y}=16 {2}/{3}= {50}/{3}..(ii)

By equation

(i) × 2 – (ii),

{2 z}/{x+y}+ {2 z}/{x-y}- {2 z}/{x-y}

=24- {50}/{3}

⇒{2 z}/{x+y}= {72-50}/{3}

= {22}/{3}=7 {1}/{3}

hours

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