In a 1500-m race, if A beats B by 100 m and B beats C by 150 m, then by what distance (in m) does A beat C?

240

It is given that A beats B by 100 m

i.e. Distance travelled by A is 1500 m and B is 1400 m respectively

So , A : B = 1500 : 1400

Similarly, the Distance travelled by B and C when B beats C is 1500 m and 1350 m respectively

B : C = 1500 : 1350

To find relation b/w A & C

\(\frac{A}{C}\) = \(\frac{A}{B}\)  × \(\frac{B}{C}\) 

\(\frac{A}{C}\) = \(\frac{1500}{1400}\)  × \(\frac{1500}{1350}\)

= \(\frac{15}{14}\)  × \(\frac{10}{9}\)

A  :  C = 150  :  126

So , If A travels 1500 meter then C will travel 1260 meter .

So , Distance by which A beats C = 1500 - 1260 = 240 meter