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:

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

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Explanation:

Let the length of race be ‘x’ meters and velocity of A,
B, C be respectively v_A, v_B and????.
According to question,
⇒x/v_A=(??−30)/v_B
⇒v_A/v_B=(x−30)/x    --------------- (i)
⇒x/v_B=(x−20)/v_C
⇒v_C/v_B=(x−20)x     --------------- (ii)
⇒x/v_A=(??−48)v_C
⇒v_C/v_A=(x−48)/x     --------------- (iii)
Multiplying eqn (i) & (ii)

x²– 48x = x² + 600 – 50x
2x = 600 ⇒ x = 300
Putting x = 300 in equation (i) & eq (ii)
⇒v_B/v_A=(300−20)/300=270/300=9/10
⇒v_B=(9/10)v_A ---------------- (v)
⇒v_C/v_B=(300−20)/300
=280/300=28/30
v_C=28/30v_B=28/30×9/10
v_A=84/100v_A-------- (vi)
From eq (v) 7 eq (vi)-
v_A: v_B: v_C = v_A (:9/10)v_A:(84/100)v_A
= 100: 90: 84 = 50: 45: 42