In a 100-m race, A beats B by 20 m and B beats C by 5 m. In the same race, find the distance by which A beats C.

`. 24 m

The correct option is 24 m.

To find the distance by which A beats C in a 100-m race, let us analyze the relative distances covered by each runner in a given time.

First, when A runs 100 m, A beats B by 20 m. This means B covers:

$100\text{m}-20\text{m}=80\text{m}$

So, the ratio of the distance covered by A to the distance covered by B is:

$\frac{\text{Distance of A}}{\text{Distance of B}}=\frac{100}{80}$

Second, when B runs 100 m, B beats C by 5 m. This means C covers:

$100\text{m}-5\text{m}=95\text{m}$

So, the ratio of the distance covered by B to the distance covered by C is:

$\frac{\text{Distance of B}}{\text{Distance of C}}=\frac{100}{95}$

Now, to find how much distance C covers when A covers 100 m, we multiply the two ratios:

$\frac{\text{Distance of A}}{\text{Distance of C}}=\left(\frac{\text{Distance of A}}{\text{Distance of B}}\right)\times \left(\frac{\text{Distance of B}}{\text{Distance of C}}\right)$

Substituting the values into the equation:

$\frac{\text{Distance of A}}{\text{Distance of C}}=\frac{100}{80}\times \frac{100}{95}$

Simplifying the fractions:

$\frac{\text{Distance of A}}{\text{Distance of C}}=\frac{5}{4}\times \frac{20}{19}=\frac{100}{76}$

This shows that when A covers 100 m, C covers 76 m.

Therefore, the distance by which A beats C in the 100-m race is:

$100\text{m}-76\text{m}=24\text{m}$