{"id":92286,"date":"2025-06-01T11:19:59","date_gmt":"2025-06-01T11:19:59","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92286"},"modified":"2025-06-01T11:19:59","modified_gmt":"2025-06-01T11:19:59","slug":"what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/","title":{"rendered":"What is the angle in degree between the hour hand and the minute hand"},"content":{"rendered":"

What is the angle in degree between the hour hand and the minute hand of a clock when the time it shows is 5:20 PM?<\/p>\n

[amp_mcq option1=”35\u00b0” option2=”40\u00b0” option3=”42\u00b0” option4=”45\u00b0” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CBI DSP LDCE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nAt 5:20 PM, the time is 5 hours and 20 minutes.
\nFirst, calculate the angle of the hour hand from the 12 o’clock position.
\nThe hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12).
\nIt also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$.
\nAt 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 \\times 60) + 20 = 300 + 20 = 320$ minutes.
\nAngle covered by hour hand = $320 \\times 0.5\u00b0 = 160\u00b0$.
\nAlternatively, angle = (5 hours $\\times$ 30\u00b0\/hour) + (20 minutes $\\times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0.<\/p>\n

Second, calculate the angle of the minute hand from the 12 o’clock position.
\nThe minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60).
\nAt 20 minutes past the hour, the minute hand is at the 20 minute mark.
\nAngle covered by minute hand = $20 \\times 6\u00b0 = 120\u00b0$.<\/p>\n

The angle between the hour hand and the minute hand is the absolute difference between their positions.
\nAngle = $|160\u00b0 – 120\u00b0| = 40\u00b0$.
\n<\/section>\n

\nThe hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H – 5.5M|$ degrees (where $5.5M = (6M – 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) – 6M| = |30H – 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 \\times 5 – 5.5 \\times 20| = |150 – 110| = 40\u00b0$.
\n<\/section>\n
\nClock problems require understanding the relative speeds of the hour and minute hands. The 12-hour mark is usually taken as the reference point (0 degrees). Angles are measured clockwise from 12.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

What is the angle in degree between the hour hand and the minute hand of a clock when the time it shows is 5:20 PM? [amp_mcq option1=”35\u00b0” option2=”40\u00b0” option3=”42\u00b0” option4=”45\u00b0” correct=”option2″] This question was previously asked in UPSC CBI DSP LDCE – 2023 Download PDFAttempt Online At 5:20 PM, the time is 5 hours and … <\/p>\n

Detailed SolutionWhat is the angle in degree between the hour hand and the minute hand<\/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":[1086],"tags":[1105,1102],"class_list":["post-92286","post","type-post","status-publish","format-standard","hentry","category-upsc-cbi-dsp-ldce","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhat is the angle in degree between the hour hand and the minute hand<\/title>\n<meta name=\"description\" content=\"At 5:20 PM, the time is 5 hours and 20 minutes. First, calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12). It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$. At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 times 60) + 20 = 300 + 20 = 320$ minutes. Angle covered by hour hand = $320 times 0.5\u00b0 = 160\u00b0$. Alternatively, angle = (5 hours $times$ 30\u00b0\/hour) + (20 minutes $times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0. Second, calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60). At 20 minutes past the hour, the minute hand is at the 20 minute mark. Angle covered by minute hand = $20 times 6\u00b0 = 120\u00b0$. The angle between the hour hand and the minute hand is the absolute difference between their positions. Angle = $|160\u00b0 - 120\u00b0| = 40\u00b0$. The hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H - 5.5M|$ degrees (where $5.5M = (6M - 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) - 6M| = |30H - 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 times 5 - 5.5 times 20| = |150 - 110| = 40\u00b0$.\" \/>\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\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the angle in degree between the hour hand and the minute hand\" \/>\n<meta property=\"og:description\" content=\"At 5:20 PM, the time is 5 hours and 20 minutes. First, calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12). It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$. At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 times 60) + 20 = 300 + 20 = 320$ minutes. Angle covered by hour hand = $320 times 0.5\u00b0 = 160\u00b0$. Alternatively, angle = (5 hours $times$ 30\u00b0\/hour) + (20 minutes $times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0. Second, calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60). At 20 minutes past the hour, the minute hand is at the 20 minute mark. Angle covered by minute hand = $20 times 6\u00b0 = 120\u00b0$. The angle between the hour hand and the minute hand is the absolute difference between their positions. Angle = $|160\u00b0 - 120\u00b0| = 40\u00b0$. The hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H - 5.5M|$ degrees (where $5.5M = (6M - 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) - 6M| = |30H - 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 times 5 - 5.5 times 20| = |150 - 110| = 40\u00b0$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:19:59+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"What is the angle in degree between the hour hand and the minute hand","description":"At 5:20 PM, the time is 5 hours and 20 minutes. First, calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12). It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$. At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 times 60) + 20 = 300 + 20 = 320$ minutes. Angle covered by hour hand = $320 times 0.5\u00b0 = 160\u00b0$. Alternatively, angle = (5 hours $times$ 30\u00b0\/hour) + (20 minutes $times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0. Second, calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60). At 20 minutes past the hour, the minute hand is at the 20 minute mark. Angle covered by minute hand = $20 times 6\u00b0 = 120\u00b0$. The angle between the hour hand and the minute hand is the absolute difference between their positions. Angle = $|160\u00b0 - 120\u00b0| = 40\u00b0$. The hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H - 5.5M|$ degrees (where $5.5M = (6M - 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) - 6M| = |30H - 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 times 5 - 5.5 times 20| = |150 - 110| = 40\u00b0$.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/","og_locale":"en_US","og_type":"article","og_title":"What is the angle in degree between the hour hand and the minute hand","og_description":"At 5:20 PM, the time is 5 hours and 20 minutes. First, calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12). It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$. At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 times 60) + 20 = 300 + 20 = 320$ minutes. Angle covered by hour hand = $320 times 0.5\u00b0 = 160\u00b0$. Alternatively, angle = (5 hours $times$ 30\u00b0\/hour) + (20 minutes $times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0. Second, calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60). At 20 minutes past the hour, the minute hand is at the 20 minute mark. Angle covered by minute hand = $20 times 6\u00b0 = 120\u00b0$. The angle between the hour hand and the minute hand is the absolute difference between their positions. Angle = $|160\u00b0 - 120\u00b0| = 40\u00b0$. The hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H - 5.5M|$ degrees (where $5.5M = (6M - 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) - 6M| = |30H - 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 times 5 - 5.5 times 20| = |150 - 110| = 40\u00b0$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:19:59+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/","url":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/","name":"What is the angle in degree between the hour hand and the minute hand","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:19:59+00:00","dateModified":"2025-06-01T11:19:59+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"At 5:20 PM, the time is 5 hours and 20 minutes. First, calculate the angle of the hour hand from the 12 o'clock position. The hour hand moves 360\u00b0 in 12 hours, or 30\u00b0 per hour (360\u00b0\/12). It also moves due to the minutes past the hour. In 60 minutes, the hour hand moves 30\u00b0. So, in 1 minute, it moves $30\u00b0\/60 = 0.5\u00b0$. At 5:20, the time is 5 hours and 20 minutes past 12. The total time in minutes past 12 is $(5 \\times 60) + 20 = 300 + 20 = 320$ minutes. Angle covered by hour hand = $320 \\times 0.5\u00b0 = 160\u00b0$. Alternatively, angle = (5 hours $\\times$ 30\u00b0\/hour) + (20 minutes $\\times$ 0.5\u00b0\/minute) = 150\u00b0 + 10\u00b0 = 160\u00b0. Second, calculate the angle of the minute hand from the 12 o'clock position. The minute hand moves 360\u00b0 in 60 minutes, or 6\u00b0 per minute (360\u00b0\/60). At 20 minutes past the hour, the minute hand is at the 20 minute mark. Angle covered by minute hand = $20 \\times 6\u00b0 = 120\u00b0$. The angle between the hour hand and the minute hand is the absolute difference between their positions. Angle = $|160\u00b0 - 120\u00b0| = 40\u00b0$. The hour hand moves 0.5\u00b0 per minute. The minute hand moves 6\u00b0 per minute. The angle between the hands at H hours and M minutes past 12 is $|30H - 5.5M|$ degrees (where $5.5M = (6M - 0.5M)$, the difference in speeds). Using the position method: Hour hand angle = $30H + 0.5M$. Minute hand angle = $6M$. Angle = $|(30H + 0.5M) - 6M| = |30H - 5.5M|$. At 5:20, H=5, M=20. Angle = $|30 \\times 5 - 5.5 \\times 20| = |150 - 110| = 40\u00b0$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/what-is-the-angle-in-degree-between-the-hour-hand-and-the-minute-hand\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CBI DSP LDCE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cbi-dsp-ldce\/"},{"@type":"ListItem","position":3,"name":"What is the angle in degree between the hour hand and the minute hand"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92286","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=92286"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92286\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}