1. Understand the Speed Ratio:
The problem states that A runs 132 times as fast as B. Let's convert this mixed fraction into an improper fraction:
132=31×3+2=35
Therefore, the ratio of the speed of A to the speed of B is:
Speed of BSpeed of A=35
This means that in the same amount of time, whenever A covers 5 meters, B covers 3 meters.
2. Relate Speed Ratio to Distance Covered:
Since Distance=Speed×Time, when the time taken is the same for both runners, the ratio of the distance covered is exactly equal to the ratio of their speeds:
Distance covered by BDistance covered by A=35
Let the distance covered by A be 5x and the distance covered by B be 3x.
3. Use the Head Start Condition:
A gives B a head start of 80 meters, and they both reach the winning post at the same time. This means that A has to run the full length of the race, while B runs 80 meters less than A.
Distance covered by A−Distance covered by B=80 m
Substitute the values of the distances in terms of x:
5x−3x=80
2x=80
x=280=40
4. Find the Total Distance of the Race:
The winning post is at the total distance that A needs to cover, which is:
Total Distance=5x
Total Distance=5×40=200 m
Correct Answer: A) 200 m
