Question : A car covers a certain distance in 25 hours. If it reduces the speed by $\frac{1}{5}$th, the car covers 200 km less in that time. The speed of the car is:
Option 1: 60 km/hr
Option 2: 30 km/hr
Option 3: 40 km/hr
Option 4: 50 km/hr
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Correct Answer: 40 km/hr
Solution :
Time taken, $t = 25$ hours
Let the initial distance be $d$ and the initial speed be $s$.
Speed = Distance ÷ Time
$s = d ÷ t$
$⇒t = \frac{d}{s}$---------------(i)
When $s$ is reduced by $\frac{s}{5}$, new $s = \frac{4s}{5}$ and $d = d - 200$,
$t = \frac{d - 200}{ \frac{4s}{5}}$ -----------------(ii)
From (i) and (ii),
$\frac{d}{s}$ = $\frac{d - 200}{ \frac{4s}{5}}$
$⇒\frac{4d}{5} = d - 200$
$⇒4d = 5d - 1000$
$⇒d = 1000$ km
$\therefore$ Speed, $s= \frac{d}{t}$ = $\frac{1000}{25}$ = 40 km/hr
Hence, the correct answer is 40 km/hr.
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