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Explanation:

In a 10 km race, A beats B by 1 km. So in the time A completes 10 km, B completes

9 km. Therefore ratio of their speeds is 10 : 9.

In a similar way, ratio of speeds of B and C is also 10 : 9

A    :  B  :  C
10  :  9
        10  :  9
100 : 90 : 81

To get a common ratio for speeds of A, B, C we take LCM of 9 and 10  which is equal to 90 (∵ B is common to both ratios) and equate corresponding values of A and C is also taking B as 90 

So if A runs 100m, C runs 81m.

So in a 10 km race, when A runs 10000 m C will run $\frac{81}{100}\times 10000$ = 8100 m 

∴ A will beat C by 10000 - 8100 or 1900 m.

Hence, 1900.