Question : In a linear race of 1000 m, A beats B by 50 m or 5 seconds. What is the difference between the speeds (in m/s) of A and B?
Option 1: $1\frac{10}{19}$
Option 2: $\frac{10}{19}$
Option 3: $\frac{9}{19}$
Option 4: $\frac{9}{10}$
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Correct Answer: $\frac{10}{19}$
Solution :
Given that in a linear race of 1000 m, A beats B by 50 m or 5 seconds.
According to the question,
When A covers 1000 m B covers 950 m
Also, B covers 50 m in 5 sec
The speed of B = $\frac{50}{5}$ = 10 m/sec
To cover 950 m B will take $\frac{950}{10}$ = 95 sec
As the time of covering 1000 m by A is the same as covering 950 m by B
So, Speed of A = $\frac{1000}{95}$
= $\frac{200}{19}$ m/sec
⇒ Difference between the speeds of A and B = $\frac{200}{19}$ – 10 = $\frac{200−190}{19}$ = $\frac{10}{19}$ m/sec
Hence, the correct answer is $\frac{10}{19}$.
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