In a race A B and C take part A beats B by 30 m B beats C by 20 m and A beats C by 48 m Which of the...........

Quantitative Aptitude (CDS) Time & distance

In a race A, B and C take part. A beats B by 30 m, B beats C by 20 m and A beats C by 48 m. Which of the following is/are correct?

1. The length of the race is 300 m.

2. The speeds of A, B and C are in the ratio 50 : 45 : 42.

Select the correct -answer using the code given below:

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

Let the length of the race be x m and A reaches the finish line after T seconds.
Therefore, Speed of A=v_A=x/T m/s

Speed of B =v_B=x-30/T m/sx
Speed of C=v_C=x-48/T m/s

Suppose B reaches the finish line after t seconds.
Speed of B =v_B=x/t m/s
Speed of C =v_C=x-20/t m/s

⇒(x−30)(x−20)=x(x−48)
⇒x²−50x+600=x²−48x
⇒2x=600⇒x=300m
Thus, the length of the race is300 m
Ratio of speeds of A, B and C=v_A:v_B:v_{C

=300 : 270 : 252 =50 : 45 :42}