Question

In a 200m race, A beats S by 20 m and N by 40 m. If S and N are running a race of 100m with exactly the same speed as before, then by how many meters will S beat?
\[\begin{align}
  & (A)\text{ 11}\text{.1 m} \\
 & \text{(B) 10 m} \\
 & \text{(C) 12 m} \\
 & \text{(D) 25 m} \\
\end{align}\]

Answer 1

Hint: We should find the distance travelled by S when A completed the race. In the similar manner, we should find the distance travelled by S when A completed the race. We were given that S and N travel with the same speed up to 100 m. So, we have to find the distance travelled by N when S travelled the remaining 100 m. Now by subtracting the distance travelled by S when N travelled 100 m with 100, we will get the distance between S and N when S completed the race.

Complete step by step solution:
From the question, we were given that A beats S by 20 m.
So, we can say that the distance travelled by S when A completed the race \[=(200-20)m=180m\].
From this we can say that the time required by A to travel 200 m is equal to time required by S to travel by 180 m.
From the question, we were given that A beats N by 40 m.
So, we can say that the distance travelled by N when A completed the race \[=(200-40)m=160m\].
From this we can say that the time required by A to travel 200 m is equal to time required by N to travel by 160 m.
In the question, it was given that S and N travelled 100m with exactly as same speed as before,
Now we should find the distance travelled by S when N travelled the 100 m.
If the distance travelled by N is equal to 160 m, then the distance travelled by S is equal to 180 m.
Let us assume the distance travelled by N is equal to x m if the distance travelled by S is equal to 100m.
By using criss-cross method, we get
\[\begin{align}
  & 160\to 180 \\
 & x\to 100 \\
\end{align}\]
\[(160)(100)=(180)(x)\]
By using cross multiplication, we get
\[x=\dfrac{(160)(100)}{(180)}=\dfrac{1600}{18}=88.889m\]
So, we get the distance between N and S \[=100-88.889=11.11m\].
 Hence, the distance between S and N is equal to 11.11m.
Therefore, option (A) is correct.

Note: Students may forget the point that S and N move with the same speed up to 100 m.
Most of the students follow the process as shown below:
If the distance travelled by N is equal to 160 m, then the distance travelled by S is equal to 180 m.
Let us assume the distance travelled by N is equal to x m if the distance travelled by S is equal to 200m.
By using criss-cross method, we get
\[\begin{align}
  & 160\to 180 \\
 & x\to 200 \\
\end{align}\]
\[(160)(200)=(180)(x)\]
By using cross multiplication, we get
\[x=\dfrac{(160)(200)}{(180)}=\dfrac{3200}{18}=177.776m\]
Then we get the distance between S and N is equal to 22.224 m.
But this is an absolutely wrong answer.
Students should read the question carefully and then they should proceed to find the correct answer. Otherwise, it may give wrong results.