A cyclist moves non stop from A to B a distance of 14 km at a certain average speed If his average s...........

Quantitative Aptitude (CDS) Time & distance

A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km/h, he takes 20 min more to cover the same distance. The original average speed of the cyclist is

5 km/h

6 km/h

7 km/h

None of these

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Explanation:

Let the original average speed of cyclist = x km/h Then, time taken to cover the distance by original average speed = 14 / $x$ hrs
A________________________________B
<------------------------14 km-------------------->
When original average speed is decreased by 1 km/h, then time taken to cover the distance = 14 / ( $x$ -1) hrs
According to the question
$\frac{14}{x}+\frac{20}{60} = \frac{14}{x-1}\:$
$=> \frac{14}{x}+\frac{1}{3} = \frac{14}{x-1}\:=>\frac{42+x}{3x}=\frac{14}{x-1}$
$=>(42+x)(x-1)=42x$
$=> 42x-42+x^{2}-x = 42x$
$=> x^{2}-x-42=0 => (x-7)(x+6)=0 => x=7 , x = -6$