Question : In a 1200 m race, bike A beats bike B by 100 m. Bike B beats bike C by 100 m in a 600 m race. If bike A beats bike C by 30 sec in a 720 m race, then what is the speed of bike C?
Option 1: $\frac{17}{3} \mathrm{~m} / \mathrm{sec}$
Option 2: $\frac{26}{9} \mathrm{~m} / \mathrm{sec}$
Option 3: $\frac{17}{9} \mathrm{~m} / \mathrm{sec}$
Option 4: $\frac{26}{3} \mathrm{~m} / \mathrm{sec}$
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Correct Answer: $\frac{17}{3} \mathrm{~m} / \mathrm{sec}$
Solution :
When bike A covers 1200 m, bike B covers 1100 m
Ratio of speed $= 12 : 11$
Also,
When bike B covers 600 m bike C covers 500 m
Ratio of speed $= 6 : 5$
The ratio of the speed of A, B, and C $= 72 : 66 : 55$
So, when bike A covers 720 m then bike C covers 550 m
⇒ Difference $= 720 - 550 = 170$ m
Now,
Bike C will cover the remaining 170 m in 30 sec
⇒ Speed of bike C $= \frac{170}{30}= \frac{17}{3}$ m / sec
Hence, the correct answer is $\frac{17}{3}$ m/sec.
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