{"id":90223,"date":"2025-06-01T10:23:24","date_gmt":"2025-06-01T10:23:24","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90223"},"modified":"2025-06-01T10:23:24","modified_gmt":"2025-06-01T10:23:24","slug":"in-an-examination-53-students-passed-in-mathematics-61-passed-in-p","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/","title":{"rendered":"In an examination, 53% students passed in Mathematics, 61% passed in P"},"content":{"rendered":"

In an examination, 53% students passed in Mathematics, 61% passed in Physics, 60% passed in Chemistry, 24% passed in Mathematics and Physics, 35% in Physics and Chemistry, 27% in Mathematics and Chemistry and 5% in none. The ratio of percentage of passes in Mathematics and Chemistry but not in Physics in relation to the percentage of passes in Physics and Chemistry but not in Mathematics is:<\/p>\n

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\nLet M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 – |None| = 100 – 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| – |M\u2229P| – |M\u2229C| – |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 – 24 – 27 – 35 + |M\u2229P\u2229C|. 95 = 174 – 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 – 88 = 7%.
\nPercentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| – |M\u2229C\u2229P| = 27% – 7% = 20%.
\nPercentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| – |M\u2229P\u2229C| = 35% – 7% = 28%.
\nThe ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7.
\n<\/section>\n
\nThis problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).
\n<\/section>\n
\nUsing a Venn diagram helps visualize the different regions. The percentage of students in M only is |M| – (|M\u2229P| + |M\u2229C|) + |M\u2229P\u2229C|. Similar calculations can be done for P only, C only, M\u2229P only, P\u2229C only, and M\u2229C only. The sum of percentages in all 7 regions plus the ‘none’ percentage should equal 100%.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

In an examination, 53% students passed in Mathematics, 61% passed in Physics, 60% passed in Chemistry, 24% passed in Mathematics and Physics, 35% in Physics and Chemistry, 27% in Mathematics and Chemistry and 5% in none. The ratio of percentage of passes in Mathematics and Chemistry but not in Physics in relation to the percentage … <\/p>\n

Detailed SolutionIn an examination, 53% students passed in Mathematics, 61% passed in P<\/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":[1114,1102],"class_list":["post-90223","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIn an examination, 53% students passed in Mathematics, 61% passed in P<\/title>\n<meta name=\"description\" content=\"Let M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 - |None| = 100 - 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| - |M\u2229P| - |M\u2229C| - |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 - 24 - 27 - 35 + |M\u2229P\u2229C|. 95 = 174 - 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 - 88 = 7%. Percentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| - |M\u2229C\u2229P| = 27% - 7% = 20%. Percentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| - |M\u2229P\u2229C| = 35% - 7% = 28%. The ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7. This problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).\" \/>\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\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In an examination, 53% students passed in Mathematics, 61% passed in P\" \/>\n<meta property=\"og:description\" content=\"Let M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 - |None| = 100 - 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| - |M\u2229P| - |M\u2229C| - |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 - 24 - 27 - 35 + |M\u2229P\u2229C|. 95 = 174 - 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 - 88 = 7%. Percentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| - |M\u2229C\u2229P| = 27% - 7% = 20%. Percentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| - |M\u2229P\u2229C| = 35% - 7% = 28%. The ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7. This problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:23:24+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":"In an examination, 53% students passed in Mathematics, 61% passed in P","description":"Let M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 - |None| = 100 - 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| - |M\u2229P| - |M\u2229C| - |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 - 24 - 27 - 35 + |M\u2229P\u2229C|. 95 = 174 - 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 - 88 = 7%. Percentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| - |M\u2229C\u2229P| = 27% - 7% = 20%. Percentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| - |M\u2229P\u2229C| = 35% - 7% = 28%. The ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7. This problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).","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\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/","og_locale":"en_US","og_type":"article","og_title":"In an examination, 53% students passed in Mathematics, 61% passed in P","og_description":"Let M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 - |None| = 100 - 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| - |M\u2229P| - |M\u2229C| - |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 - 24 - 27 - 35 + |M\u2229P\u2229C|. 95 = 174 - 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 - 88 = 7%. Percentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| - |M\u2229C\u2229P| = 27% - 7% = 20%. Percentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| - |M\u2229P\u2229C| = 35% - 7% = 28%. The ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7. This problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:23:24+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/","url":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/","name":"In an examination, 53% students passed in Mathematics, 61% passed in P","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:23:24+00:00","dateModified":"2025-06-01T10:23:24+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let M, P, and C represent the sets of students who passed in Mathematics, Physics, and Chemistry, respectively. We are given the following percentages: |M|=53, |P|=61, |C|=60, |M\u2229P|=24, |P\u2229C|=35, |M\u2229C|=27, |None|=5. The percentage of students who passed in at least one subject is |M\u222aP\u222aC| = 100 - |None| = 100 - 5 = 95%. Using the principle of inclusion-exclusion: |M\u222aP\u222aC| = |M| + |P| + |C| - |M\u2229P| - |M\u2229C| - |P\u2229C| + |M\u2229P\u2229C|. So, 95 = 53 + 61 + 60 - 24 - 27 - 35 + |M\u2229P\u2229C|. 95 = 174 - 86 + |M\u2229P\u2229C|. 95 = 88 + |M\u2229P\u2229C|. Thus, |M\u2229P\u2229C| = 95 - 88 = 7%. Percentage of passes in Mathematics and Chemistry but not in Physics is the region (M\u2229C) excluding the triple intersection (M\u2229C\u2229P). This is |M\u2229C| - |M\u2229C\u2229P| = 27% - 7% = 20%. Percentage of passes in Physics and Chemistry but not in Mathematics is the region (P\u2229C) excluding the triple intersection (M\u2229P\u2229C). This is |P\u2229C| - |M\u2229P\u2229C| = 35% - 7% = 28%. The ratio of the percentage of passes in Mathematics and Chemistry but not in Physics to the percentage of passes in Physics and Chemistry but not in Mathematics is 20 : 28. Simplifying the ratio by dividing by 4, we get 5 : 7. This problem requires using the principle of inclusion-exclusion for three sets and calculating the percentages corresponding to specific regions in a Venn diagram (intersections of two sets excluding the third).","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-53-students-passed-in-mathematics-61-passed-in-p\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"In an examination, 53% students passed in Mathematics, 61% passed in P"}]},{"@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\/90223","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=90223"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90223\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}