SSC CGL 17 Aug 2021 Shift 3 Paper

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Question : 65 of 100

Marks: +1, -0

A man can row a distance of

8 {km}

downstream in a certain time and can row

6 {km}

upstream in the same time. If he rows

24 {km}

upstream and the same distance downstream in

1 \;{3}/{4} {h}

, then the speed (in

{km} \/ {h}

) of the current is

$4 \;{1}/{2}$
4
3
$2 \;{1}/{2}$

Solution:

Let the speed of boat

=x {km} \/ {h}

and the speed of current

=y {km} \/ {h}

We know that,

\;\text " Speed "\;=\;{\;\text " Distance "\;}/{\;\text " Time "\;}

According to the question,

\;\; \;{8}/{x+y} \;\; =\;{6}/{x-y}

⇒ \;\; 8 x-8 y \;\; =6 x+6 y

⇒ \;\; 2 x \;\; =14 y ⇒ x=7 y

\;\;\text " Now "\;, \;{24}/{(x-y)}+\;{24}/{(x+y)}=\;{7}/{4}

⇒ \;\; \;{24(x+y+x-y)}/{(x^{2}-y^{2})}=\;{7}/{4}

⇒ \;\; \;{24(2 x)}/{(x^{2}-y^{2})}=\;{7}/{4}

⇒ \;\; \;{24 × 2 × 7 y}/{(7 y)^{2}-y^{2}}=\;{7}/{4}

⇒ \;\; \;{48 × 7 y}/{48 y^{2}}=\;{7}/{4}

∴ \;\; y=4 {km} \/ {h}

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