In a race of 600 , m,A can beat B by 60 , m a | vedclass

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(C) When $A$ runs $600 \, m$,$B$ runs $600 - 60 = 540 \, m$. The ratio of speeds of $A$ and $B$ is $A:B = 600:540 = 10:9$.When $B$ runs $500 \, m$,$C$

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(C) When $A$ runs $600 \, m$,$B$ runs $600 - 60 = 540 \, m$. The ratio of speeds of $A$ and $B$ is $A:B = 600:540 = 10:9$.When $B$ runs $500 \, m$,$C$ runs $500 - 50 = 450 \, m$. The ratio of speeds of $B$ and $C$ is $B:C = 500:450 = 10:9$.To find the ratio $A:B:C$,we equate the $B$ component: $A:B = 100:90$ and $B:C = 90:81$. Thus,$A:B:C = 100:90:81$.In a race of $400 \, m$,$A$ covers $400 \, m$. Since the ratio of $A$ to $C$ is $100:81$,when $A$ covers $400 \, m$,$C$ covers $C = \frac{81}{100} 	imes 400 = 324 \, m$.Therefore,$A$ beats $C$ by $400 - 324 = 76 \, m$.

In a race of $600 \, m$,$A$ can beat $B$ by $60 \, m$ and in a race of $500 \, m$,$B$ can beat $C$ by $50 \, m$. By how many meters will $A$ beat $C$ in a race of $400 \, m$?

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