{"id":89560,"date":"2025-06-01T10:06:59","date_gmt":"2025-06-01T10:06:59","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89560"},"modified":"2025-06-01T10:06:59","modified_gmt":"2025-06-01T10:06:59","slug":"a-and-b-take-part-in-100-meters-race-where-a-beats-b-by-10-meters-to","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-take-part-in-100-meters-race-where-a-beats-b-by-10-meters-to\/","title":{"rendered":"A and B take part in 100 meters race, where A beats B by 10 meters. To"},"content":{"rendered":"

A and B take part in 100 meters race, where A beats B by 10 meters. To favour B, A starts 10 meters behind the starting line in a second 100 meters race, running at their earlier speeds. Which one among the following is true in view of the second race?<\/p>\n

[amp_mcq option1=”A and B reach the finishing line simultaneously” option2=”B beats A by 1 meter” option3=”B beats A by 2 meters” option4=”A beats B by 1 meter” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2012<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is D, indicating A beats B by 1 meter in the second race.
\n<\/section>\n
\nIn the first race, A beats B by 10 meters in a 100-meter race. This allows us to determine the relative speeds of A and B. In the second race, A starts 10 meters behind the line and runs 110 meters, while B runs 100 meters, and they maintain their earlier speeds. We need to compare their finish times.
\n<\/section>\n
\nLet the length of the race track be $L = 100$ meters.
\nIn the first race, A runs 100m and B runs 90m in the same time, say T.
\nSpeed of A, $V_A = 100 \/ T$.
\nSpeed of B, $V_B = 90 \/ T$.
\nRatio of speeds: $V_A \/ V_B = (100\/T) \/ (90\/T) = 100\/90 = 10\/9$. So, $V_A = (10\/9) V_B$.<\/p>\n

In the second race, the finish line is 100 meters from the standard starting line.
\nA starts 10 meters behind the starting line, so A has to run $100 + 10 = 110$ meters to reach the finish line.
\nB starts at the regular starting line, so B has to run 100 meters to reach the finish line.<\/p>\n

Time taken by A to cover 110 meters: $T_A = \\text{Distance} \/ \\text{Speed} = 110 \/ V_A$.
\nTime taken by B to cover 100 meters: $T_B = \\text{Distance} \/ \\text{Speed} = 100 \/ V_B$.<\/p>\n

Substitute $V_A = (10\/9) V_B$ into the expression for $T_A$:
\n$T_A = 110 \/ ((10\/9) V_B) = (110 \\times 9) \/ (10 \\times V_B) = 990 \/ (10 V_B) = 99 \/ V_B$.<\/p>\n

Now compare $T_A$ and $T_B$:
\n$T_A = 99 \/ V_B$ and $T_B = 100 \/ V_B$.
\nSince $99 < 100$ and $V_B$ is positive, $T_A < T_B$. A reaches the finish line faster than B. A beats B.\n\nTo find by how much A beats B, calculate the distance covered by B when A finishes the race (at time $T_A$).\nDistance covered by B at time $T_A$ is $D_B = V_B \\times T_A = V_B \\times (99 \/ V_B) = 99$ meters.\nWhen A crosses the finish line, B has covered 99 meters from their starting line. The finish line is at 100 meters for B.\nSo, B is $100 - 99 = 1$ meter behind the finish line when A finishes.\nA beats B by 1 meter.\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A and B take part in 100 meters race, where A beats B by 10 meters. To favour B, A starts 10 meters behind the starting line in a second 100 meters race, running at their earlier speeds. Which one among the following is true in view of the second race? [amp_mcq option1=”A and B … <\/p>\n

Detailed SolutionA and B take part in 100 meters race, where A beats B by 10 meters. To<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1116,1102],"class_list":["post-89560","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1116","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA and B take part in 100 meters race, where A beats B by 10 meters. To<\/title>\n<meta name=\"description\" content=\"The correct option is D, indicating A beats B by 1 meter in the second race. In the first race, A beats B by 10 meters in a 100-meter race. This allows us to determine the relative speeds of A and B. In the second race, A starts 10 meters behind the line and runs 110 meters, while B runs 100 meters, and they maintain their earlier speeds. We need to compare their finish times.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-take-part-in-100-meters-race-where-a-beats-b-by-10-meters-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A and B take part in 100 meters race, where A beats B by 10 meters. To\" \/>\n<meta property=\"og:description\" content=\"The correct option is D, indicating A beats B by 1 meter in the second race. In the first race, A beats B by 10 meters in a 100-meter race. This allows us to determine the relative speeds of A and B. In the second race, A starts 10 meters behind the line and runs 110 meters, while B runs 100 meters, and they maintain their earlier speeds. We need to compare their finish times.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-take-part-in-100-meters-race-where-a-beats-b-by-10-meters-to\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:06:59+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A and B take part in 100 meters race, where A beats B by 10 meters. To","description":"The correct option is D, indicating A beats B by 1 meter in the second race. In the first race, A beats B by 10 meters in a 100-meter race. 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