# Run Race MCQ 2( running ratios, 100 meters run race)

Run Race MCQ 2: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by________?

a) 21 m           b) 26 m       c) 28 m       d) 29 m

Solution:

Lets suppose that there is 100 meters run race.

So, by inference from  given data we can say;

if A runs 100 m then B will be at 75 meters

i-e A:B=100:75

or

$\frac{A}{B}=\frac{100}{75}=\frac{4}{3}$ —-1

If Bruns 100 m then C will be at 96 m

i-e

B:C=100:96

or

$\frac{B}{C}=\frac{100}{96}=\frac{25}{24}$ —–2

We have to find at what ration A beats C! or we have to find A:C=?

We can write;

$\frac{A}{C}=\frac{A}{B}\times \frac{B}{C}$

Putting values from eq 1 & 2 above;

we get;

$\frac{A}{C}=\frac{25}{24}\times \frac{4}{3}= \frac {100}{72}$

i-e

A:C= 100:72

In other words, If A runs 100 m then C will be at 72 m

i-e A will beat C by 100-72=28 m

So, the option C is the answer!

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