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# The distance covered for a race is 1km. When A and B run the race, A wins by 40 meters when A and C run, then A wins by 70 meters. When B and C run(a) B wins by 110m(b) C wins by 100m(c) B wins by 314m(d) C wins by 50m

Last updated date: 19th Jul 2024
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Hint: For solving this question you should know about the calculating distance by comparisons and ratios. In this problem we will find the comparison ratio between A and B and then we find the same distance ratio for A and C. And then with the relationship ratio of these we find the distance for which B and C run for winning.

According to our question it is given that the distance covered for a race is 1km. When A and B run the race, A wins by 40 meters, when A and C run, then A wins by 70 meters. Then find the right option for B and C run.
As we know that if two or more than two parameters are given to calculate any third parameter on the same scale then we find the third one by comparing and by taking ratios of those with one another.
So, if we see our question, it is given that if A and B run then A wins by 40 meters.
So, we can write it as,
$A:B=1000:960$
And when A and C run then A wins by 70 meters.
So, we can write $A:C=1000:930$
So, when B and C run,
B win by C $=\dfrac{960-930}{960}\times 1000$
B win by C $=\dfrac{30}{960}\times 1000$
B win by C $=31\dfrac{1}{4}$m

So, the correct answer is “Option c”.

Note: While solving these types of questions you should know about the taking right component with right in the ratios. Because we can only find the right answer if the ratio of two is right. And the comparison of that will be given a final right answer.