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.

Given:

A can beat B by 20 m in a race of total distance = 100 m

B can beat C by 5 m in a race of total distance = 100 m.

Concept used:

A's Speed = Distance / Time      (for same time, speed is directly proportional to distance travelled.)

Calculation:

Distance travelled by A = 100m

Distance travelled by B when A beats B by 20m

= 100 - 20 

= 80 m.

Distance travelled by B when B beats C by 5 m in a race of 100 m = 100m.

Distance travelled by C when B beats C by 5 m in a race of 100 m

= 100 - 5

= 95 m.

Ratio of speeds of A and B will be in the ratio of their distances

= 100 : 80 

= 5 : 4 .... (1)

Ratio of speeds of B and C will be in the ratio of their distances

= 100 : 95

= 20 : 19 ... (2)

Making the ratio for B same in both (1) and (2), we multiply (1) by 5

= 5 × 5 : 4 × 5

= 25 : 20 ... (3)

Combining (2) and (3) we get ratio of speeds of A, B and C 

= 25 : 20 : 19.

When A travels 100 m, C will travel

= 25 × 4 : 20 × 4 : 19 × 4

= 100 : 80 : 76

When A travels 100 m, C travels 76 m.

∴ A will beat C by 24 m.