Question

If a train runs at 40 Km/hr, it reaches its destination late by 11 minutes, but if it runs at 50 km/hr, it is late by 5 minutes only. The correct time for the train to complete its journey is
A) 13 min
B) 15 min
C) 19 min
D) 21 min

Answer 1

Hint: Think of the basic definition of speed and focus on the point that the speed mentioned here is the average speed. Assume actual time and distance then we know that distance will remain the same for both the cases, using this information we will get the solution.

Complete step-by-step answer:
Average speed is defined as the total distance covered by a body divided by the time taken by the body to cover it.
$\therefore {{v}_{avg}}=\dfrac{\text{distance covered}}{\text{time taken}}$
Now, starting with the solution to the above question. Let the actual time taken be t hours and the distance to be travelled be x km.
When the train was moving with a speed of 40 km/hour, it takes 11 min i.e. $\dfrac{11}{60}\text{ hours}$ more than the actual time. We can represent this in the form of mathematical equation as:
${{v}_{avg}}=\dfrac{\text{distance covered}}{\text{time taken}}$
$\Rightarrow 40=\dfrac{x}{\text{t+}\dfrac{11}{60}}.............(i)$
Also, it is mentioned that when the train was moving with a speed of 50 km/hour, it takes 5 min, i.e., $\dfrac{5}{60}\text{ hours}$ more than the actual time. We can represent this in the form of mathematical equation as:
${{v}_{avg}}=\dfrac{\text{distance covered}}{\text{time taken}}$
$\Rightarrow 50=\dfrac{x}{\text{t+}\dfrac{5}{60}}.............(ii)$
Now we will divide equation (ii) by equation (i). On doing so, we get
$\dfrac{50}{40}=\dfrac{\dfrac{x}{\text{t+}\dfrac{5}{60}}}{\dfrac{x}{t+\dfrac{11}{60}}}$
$\Rightarrow \dfrac{5}{4}=\dfrac{t+\dfrac{11}{60}}{t+\dfrac{5}{60}}$
Now to further solve the equation, we will cross-multiply. On cross-multiplication, we get
$5\left( t+\dfrac{5}{60} \right)=4\left( t+\dfrac{11}{60} \right)$
$\Rightarrow 5t+\dfrac{25}{60}=4t+\dfrac{44}{60}$
$\Rightarrow t=\dfrac{19}{60}\text{ hours = 19 minutes}$
Therefore, the actual time train should take is 19 minutes. Hence, we can say that option (C) is the correct answer.

Note: Make sure that you convert all the elements required for solving the problem to a standard unit system to avoid errors, as we did in the above solution by converting time to hours.