Question : In a 100-m race, A beats B by 20 m and B beats C by 5 m. In the same race, A beats C by:

Option 1: 26 m

Option 2: 22 m

Option 3: 25 m

Option 4: 24 m

Correct Answer: 24 m

Solution : Distance travelled by A = 100 m
Distance travelled by B when A beats B by 20 m = 100 – 20  = 80 m.
Distance travelled by B when B beats C by 5 m in a race of 100 m = 100 m.
Distance travelled by C when B beats C by 5 m in a race of 100 m = 100 – 5 = 95 m
The ratio of speeds of A and B will be in the ratio of their distances = 100 : 80
= 5 : 4 ---(1)
The 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 the 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.
$\therefore$  A will beat C by 24 m.
Hence, the correct answer is 24 m.