Question

A train covered a certain distance at a uniform speed. If the train would have been 10km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10km/h ; it would have taken 3 hours more than the scheduled time. The distance covered by the train is ..................

• A. $600km.$
• B. $400km.$
• C. $260km.$
• D. $300km.$

Answer 1

Answer: (A)

Let the speed of the train be $x$ km/h and the time has taken be $y$ h.
The total distance is then $xy$ km.
Case1:
Speed increases by $10$ km/h and the time taken reduces by $2$ hours.

The distance traveled remains $xy$ km.
$(x+10)(y-2)=xy$
Therefore, $xy-2x+10y-20=xy$
$\Rightarrow -2x+10y-20=0$
$\Rightarrow -2x+10y=20$ ---------- (1)
Case 2:
Speed decreases by $10$ km/h, then the time taken increases by $3$ hours.

However, the distance remains,$xy$ km.
$(x-10)(y+3)=xy$
Therefore, $xy+3x-10y-30=xy$
$\Rightarrow 3x-10y-30=0$
$\Rightarrow 3x-10y=30$ ---------- (2)
$\Rightarrow x=50$ km/h
Using this in (2), we get
$150-10y=30$
$\Rightarrow y=12$
Therefore, the distance is $50\times 12=600$ km.