In a km race A can beat B by 100 m

=> While A run 1000 m, B run $\left(1000-100\right)$=900 m

In a km race B can beat C by 60 m

=> While B runs 1000 m, C runs $\left(1000-60\right)$=940 m

$\text{ => While B run 1 m, C run }\dfrac{940}{1000}\text{ m}$

$\text{ => While B runs 900 m, C runs }\dfrac{940}{1000} \times 900 = 94 \times 9 = 846\text{ m}$

i.e., while A run 1000 m, C run 846 m

Hence, A can beat C by $\left(1000-846\right)$= 154 m