Two friends A and B, with speed in the ratio 4:1, are running on track

1.	Two friends A and B, with speed in the ratio 4:1, are running on track PQ. A starts from P towards Q and when he reaches point exactly in the middle of the track, B starts running from P towards Q. A reaches Q turns back and continues towards P and meets B at a distance of 175 m from Q. What is the total length of the track? 1. 250 m2. 275 m3. 225 m4. 200 m
Answer» Correct Answer - Option 1 : 250 m Let 4x and x be the speeds(m/s) of A and B respectively and L be the length(m) of track. Let d be the distance travelled by B towards Q from P, when A reaches Q from the mid-point. As we know, distance covered is directly proportional to the speed if the time taken is constant. Thus, (L/2):d = 4:1 ⇒ d = L/8 Similarly, 175:(L – d – 175) = 4:1 ⇒ 175 = 4 × (7L/8 – 175) ⇒ 7L/2 = 5 × 175 ⇒ L = 10 × 25 = 250 m

Two friends A and B, with speed in the ratio 4:1, are running on track PQ. A starts from P towards Q and when he reaches point exactly in the middle of the track, B starts running from P towards Q. A reaches Q turns back and continues towards P and meets B at a distance of 175 m from Q. What is the total length of the track? 1. 250 m2. 275 m3. 225 m4. 200 m

Answer» Correct Answer - Option 1 : 250 m

Let 4x and x be the speeds(m/s) of A and B respectively and L be the length(m) of track.

Let d be the distance travelled by B towards Q from P, when A reaches Q from the mid-point.

As we know, distance covered is directly proportional to the speed if the time taken is constant.

Thus, (L/2):d = 4:1 ⇒ d = L/8

Similarly, 175:(L – d – 175) = 4:1

⇒ 175 = 4 × (7L/8 – 175)

⇒ 7L/2 = 5 × 175

⇒ L = 10 × 25 = 250 m

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