Question & Answer
QUESTION

In a kilometer race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 metres, the time taken by A to run 1 kilometer is
A.250 seconds
B.205 seconds
C.200 seconds
D.210 seconds

ANSWER Verified Verified
Hint- Let’s apply the conditions given in the problem and make equations with respect to that. Then calculate the difference in times of A and C to get the answer to this problem.
We’ll use the formula of speed,
${\text{Speed = }}\dfrac{{{\text{Distance}}}}{{{\text{time}}}}$

Complete step-by-step answer:

So, according to question A beats B by 30 seconds and B beats C by 15 seconds.
Therefore, A beats C by= (30+15) seconds=45 seconds.
As given A beats C by 180 meters and time taken by C to cover this distance is 45 seconds.
Therefore speed of C =$\dfrac{{{\text{Distance}}}}{{{\text{time}}}}$=$\dfrac{{180}}{{45}} = 4$ m/sec.
And total distance of race = 1 Km =1000m
Therefore time taken by C to cover total distance =$\dfrac{{{\text{Distance}}}}{{{\text{time}}}}$=$\dfrac{{1000}}{4}$=250 seconds
And since A beats C by 45 seconds, Therefore time taken by A =250-45
=205 seconds

Note - While considering any of the values of speed, distance, and time for calculation, make sure the units of all of them are the same. Otherwise, it will lead to an incorrect calculation.