A train covers a distance of 56 km in 35 minutes. Travelling at the same speed, in how many seconds will the train cover a distance of 720 metres?

The correct answer is 27.

To find the time taken by the train to cover a distance of 720 metres at the same speed, we first need to determine the speed of the train in standard units (metres per second, or m/s).

Step 1: Calculate the speed of the train.
The train covers a distance of 56 km in 35 minutes.
Let us convert the distance from kilometres (km) to metres (m):
Distance = 56 km = 56 × 1000 m = 56,000 m

Now, let us convert the time from minutes to seconds:
Time = 35 minutes = 35 × 60 seconds = 2100 seconds

Using the formula for speed:
Speed = Distance / Time
We get:
$\mathrm{Speed}=\frac{56000}{2100}\mathrm{m/s}$
Simplifying the fraction by dividing the numerator and the denominator by 100:
$\mathrm{Speed}=\frac{560}{21}\mathrm{m/s}$
Further simplifying by dividing both numbers by 7:
$\mathrm{Speed}=\frac{80}{3}\mathrm{m/s}$

Step 2: Calculate the time required to cover 720 metres.
We are given that the new distance to be covered is 720 metres.
Using the relation:
Time = Distance / Speed
We substitute the distance (720 m) and the speed (80/3 m/s) into the formula:
$\mathrm{Time}=\frac{720}{\left(\frac{80}{3}\right)}$
To divide by a fraction, we multiply by its reciprocal:
$\mathrm{Time}=720\times \frac{3}{80}$
Simplifying the calculation:
$\mathrm{Time}=\left(\frac{720}{80}\right)\times 3$
Since 720 divided by 80 is 9, we have:
Time = 9 × 3 = 27 seconds

Therefore, the train will cover a distance of 720 metres in 27 seconds.