Question

An aeroplane covers a certain distance at a speed of 240 km/hr in 5 hours. To covers the same distance in $1\dfrac{2}{3}$ hours, it must travel at a speed of:
A. 300 km/hr
B. 360 km/hr
C. 600 km/hr
D. 720 km/hr

Answer 1

Hint: In this question, the time taken by the aeroplane is changing but the distance travelled by the aeroplane is fixed. We know that speed =$\dfrac{{{\text{distance travelled}}}}{{{\text{time taken}}}}$. So use the relation that speed is inversely proportional to the time taken.

Complete step-by-step answer:

In the question we have given:
Time taken is changing from 5 hours to $1\dfrac{2}{3}$ hours. And distance travelled by the aeroplane is fixed. We have to calculate the speed for which time taken is $1\dfrac{2}{3}$ hours.
We know the relationship between speed, distance travelled and time taken is given by:
${\text{Speed(S) = }}\dfrac{{{\text{Distance travelled(D)}}}}{{{\text{Time taken(t)}}}}.$
And we know that distance is constant. So we can write:
 $
  {\text{speed = }}\dfrac{{\text{k}}}{{{\text{time taken}}}} \\
   \Rightarrow \dfrac{{{{\text{s}}_1}}}{{{{\text{s}}_2}}} = \dfrac{{{{\text{t}}_2}}}{{{{\text{t}}_1}}} \\
 $ (1)
Where
k is a constant.
${t_1}$ is the time taken to travel the distance at a speed of 240 km/hr = 5 hours.

${t_2}$ is the time taken to travel the distance at a new speed = $1\dfrac{2}{3} = \dfrac{5}{3}$ hours.
Let the new speed be x km/hr.
Putting the values of time and speed for the two cases in equation 1, we get:
$
  \dfrac{{{{\text{s}}_1}}}{{{{\text{s}}_2}}} = \dfrac{{{t_2}}}{{{t_1}}} \\
   \Rightarrow \dfrac{{240}}{{\text{x}}} = \dfrac{{\dfrac{5}{3}}}{5} = \dfrac{1}{3} \\
   \Rightarrow {\text{x = 240}} \times {\text{3 = 720}} \\
 $
Therefore the new speed is 720 km/hr.
So option D is correct.

Note: One thing is clear that previously the aeroplane was travelling a specific distance in 5 hours, but now the same distance needs to be covered in a lesser time so applying general sense we know that it must boost its speed, so any option depicting speed lesser than the given initial speed can directly be discarded.