Question

In \[{\mathbf{100m}}\] race, A covers the distance in \[{\mathbf{36}}\] seconds and B in \[{\mathbf{45}}\] seconds. In this race A beats B by:
${
  A.20m \\
  B.25m \\
  C.22.5m \\
  D.9m \\
} $

Answer 1

Hint: In the given question, we have to find out the value of distance by which $A$ beats $B$. To solve this question, find out the distance covered by both players and time taken by the winner to reach its goal. Since distance is given. Find out their speeds. $A$ covers $100m$ in \[36\]secs. Find out the distance covered out by \[B\] in \[36\]secs. The answer you will get, subtract it by \[100m\] as \[100m/s\] distance covered \[A\] by that time. You will get the resultant answer.

Complete step-by-step answer:
Total distance given \[100m\].
Time taken by \[A = 36\]secs.
\[\therefore \]Speed of \[A = \]Distance covered / Time taken
\[ = \dfrac{{100}}{{36}}m/s\]
Again, Distance covered by \[B = 100m\].
Time taken by \[B = 45\]secs.
\[\therefore \]Speed of \[B = \]Distance covered / Time taken
\[ = \dfrac{{100}}{{45}}m/s\]
Now, distance covered by \[B\] in \[36\]secs. –
\[ = \]speed\[ \times \]time
\[ = \left( {\dfrac{{100}}{{45}} \times 36} \right)m\]
\[ = 80m\]
\[\therefore B\]covered in \[80m\] in \[36\]secs while \[A\] covers \[100m\] in \[36\]secs.
So, to get the distance by which A beats B, we will have to distinguish between the distance covered by A & B.
\[\therefore A\] Beats \[B\] by \[\left( {100 - 80} \right)m = 20m\].

Hence, option \[A\] is correct.

Note: This question was asked and related to an arithmetic topic named – ‘Distance, Speed and Time’. Most of the questions of this topic are solved by using an important form, Distance \[ = \]speed\[ \times \]time. Other two formulae, speed and time derived from this relation. While substituting the values we must check the units. We should not consider the distance covered by one quantity in ‘km’ and the distance covered by another quantity in ‘m’.