Question : A train covers 400 km at a uniform speed. If the speed had been 10 km/hr more, it would have taken 2 hours less for the same journey. What is the usual time taken (in hours) by it to complete the journey?
Option 1: 12
Option 2: 15
Option 3: 8
Option 4: 10
Correct Answer: 10
Solution :
Distance = 400 km
Let the speed be $s$ and the time taken be $t$.
$400 = s × t$ -------------------(i)
If speed = $s+10$,
time taken = $t-2$
Distance = $(s+10)(t-2)$
$400 = (s+10)(t-2)$ ------------------(ii)
From equations (i) and (ii),
$ s × t = (s+10)(t-2)$
⇒ $st = st+ 10t-2s-20$
⇒ $10t = 2s+20$
⇒ $5t = s+10$
⇒ $5 (\frac{400}{s}) = s + 10$
⇒ $s^2 + 10s - 2000 = 0$
⇒ $s^2+50s -40s - 2000 = 0$
⇒ $(s+50)(s-40) = 0$
$\therefore s = 40,-50$
Speed cannot be negative, so, Speed, $s$ = 40 km/hr
Time, $t =\frac{400}{40} = 10$ hours
Hence, the correct answer is 10.
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