In a 100-meter race, X runs at 5 m/s and Y at 4 m/s. How much head start should X give Y (in meters) so that the race ends in a tie?

The correct option is 20.

Step-by-Step Explanation:

Step 1: Calculate the time taken by X to finish the race.

The total distance of the race is 100 meters, and X runs at a speed of 5 m/s.

Using the formula for time:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

For X:

${\text{Time}}_{\text{X}}=\frac{100\text{m}}{5\text{m/s}}=20\text{seconds}$

Step 2: Calculate the distance Y can cover in that same time.

For the race to end in a tie, both X and Y must cross the finish line at the exact same moment. Therefore, Y also has 20 seconds to reach the finish line.

Y's speed is 4 m/s.

Using the formula for distance:

$\text{Distance}=\text{Speed}\×\text{Time}$

For Y in 20 seconds:

${\text{Distance}}_{\text{Y}}=4\text{m/s}\×20\text{s}=80\text{meters}$

Step 3: Determine the required head start.

Since Y can cover 80 meters in the 20 seconds it takes X to complete the full 100 meters, X must give Y a head start equal to the remaining distance of the race.

$\text{Head Start}=100\text{m}-80\text{m}=20\text{meters}$

Thus, X should give Y a head start of 20 meters so that the race ends in a tie.