During a 1200-meter charity run, three friends — Ravi, Sohan, and Tariq — run at different constant speeds. When Ravi finishes 1200 meters, Sohan has covered 1140 meters, and Tariq has covered 1110 meters.

Consider the following statements:
Statement I: In a 1200-meter race between Sohan and Tariq, Sohan should give Tariq a 75-meter head start for a fair race.
Statement II: The speed ratio of Sohan to Tariq is 114:111.

Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

During a 1200-meter charity run, three friends &mdash; Ravi, Sohan, and Tariq &mdash; run at different constant speeds. When Ravi finishes 1200 meters, Sohan has covered 1140 meters, and Tariq has covered 1110 meters.

Consider the following statements:
Statement I: In a 1200-meter race between Sohan and Tariq, Sohan should give Tariq a 75-meter head start for a fair race.
Statement II: The speed ratio of Sohan to Tariq is 114:111.

Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

ONLiNE UPSC · Accepted Answer

When Ravi runs 1200 m:
Sohan runs 1140 m &rarr; Speed ratio of Sohan to Ravi = 1140 : 1200 = 19 : 20
Tariq runs 1110 m &rarr; Speed ratio of Tariq to Ravi = 1110 : 1200 = 37 : 40
So, speed ratio of Sohan to Tariq = (19/20) &divide; (37/40) = (19&times;40) / (20&times;37) = 760 / 740 = 38 : 37.
Let the total race length be 1200 m. For a fair race, Sohan should cover the full 1200 m while Tariq runs 1200 m &times; (37/38) = 1168.42 m
Head start = 1200 &ndash; 1168.42 &asymp; 31.58 m &rarr; Not 75 m
Statement I is incorrect
Statement II is correct (114:111 is 38:37)
Hence, option b is correct.

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M Question 1	⏱ 0
During a 1200-meter charity run, three friends — Ravi, Sohan, and Tariq — run at different constant speeds. When Ravi finishes 1200 meters, Sohan has covered 1140 meters, and Tariq has covered 1110 meters. Consider the following statements: Statement I: In a 1200-meter race between Sohan and Tariq, Sohan should give Tariq a 75-meter head start for a fair race. Statement II: The speed ratio of Sohan to Tariq is 114:111. Select the correct answer from the options below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.