{"id":90179,"date":"2025-06-01T10:22:22","date_gmt":"2025-06-01T10:22:22","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90179"},"modified":"2025-06-01T10:22:22","modified_gmt":"2025-06-01T10:22:22","slug":"in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/","title":{"rendered":"In an examination, 25% of the candidates failed in Mathematics and 12%"},"content":{"rendered":"

In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination ?<\/p>\n

[amp_mcq option1=”300″ option2=”400″ option3=”460″ option4=”500″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is B) 400.
\n<\/section>\n
\nLet M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both.
\nGiven: M = 25%, E = 12%, B = 10%.
\nThe percentage of candidates who failed in at least one subject is given by the formula:
\nP(M U E) = P(M) + P(E) – P(M \u2229 E)
\nPercentage failed in at least one subject = 25% + 12% – 10% = 37% – 10% = 27%.
\nThe percentage of candidates who passed in both subjects is the remaining percentage:
\nPercentage passed in both = 100% – Percentage failed in at least one subject = 100% – 27% = 73%.
\nWe are given that 292 candidates passed in both subjects.
\nLet T be the total number of candidates.
\nSo, 73% of T = 292
\n(73 \/ 100) * T = 292
\nT = (292 * 100) \/ 73
\nT = 29200 \/ 73
\nDividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292).
\nSo, 29200 \/ 73 = 400.
\nThe total number of candidates is 400.
\n<\/section>\n
\nThis problem uses the principle of inclusion-exclusion for calculating the union of two sets (failures in Mathematics and English). The complement of the set of people failing in at least one subject is the set of people passing in both subjects.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

In an examination, 25% of the candidates failed in Mathematics and 12% failed in English. If 10% of the candidates failed in both the subjects and 292 candidates passed in both the subjects, which one of the following is the number of total candidates appeared in the examination ? [amp_mcq option1=”300″ option2=”400″ option3=”460″ option4=”500″ correct=”option2″] … <\/p>\n

Detailed SolutionIn an examination, 25% of the candidates failed in Mathematics and 12%<\/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":[1101,1102],"class_list":["post-90179","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIn an examination, 25% of the candidates failed in Mathematics and 12%<\/title>\n<meta name=\"description\" content=\"The correct answer is B) 400. Let M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both. Given: M = 25%, E = 12%, B = 10%. The percentage of candidates who failed in at least one subject is given by the formula: P(M U E) = P(M) + P(E) - P(M \u2229 E) Percentage failed in at least one subject = 25% + 12% - 10% = 37% - 10% = 27%. The percentage of candidates who passed in both subjects is the remaining percentage: Percentage passed in both = 100% - Percentage failed in at least one subject = 100% - 27% = 73%. We are given that 292 candidates passed in both subjects. Let T be the total number of candidates. So, 73% of T = 292 (73 \/ 100) * T = 292 T = (292 * 100) \/ 73 T = 29200 \/ 73 Dividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292). So, 29200 \/ 73 = 400. The total number of candidates is 400.\" \/>\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-25-of-the-candidates-failed-in-mathematics-and-12\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In an examination, 25% of the candidates failed in Mathematics and 12%\" \/>\n<meta property=\"og:description\" content=\"The correct answer is B) 400. Let M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both. Given: M = 25%, E = 12%, B = 10%. The percentage of candidates who failed in at least one subject is given by the formula: P(M U E) = P(M) + P(E) - P(M \u2229 E) Percentage failed in at least one subject = 25% + 12% - 10% = 37% - 10% = 27%. The percentage of candidates who passed in both subjects is the remaining percentage: Percentage passed in both = 100% - Percentage failed in at least one subject = 100% - 27% = 73%. We are given that 292 candidates passed in both subjects. Let T be the total number of candidates. So, 73% of T = 292 (73 \/ 100) * T = 292 T = (292 * 100) \/ 73 T = 29200 \/ 73 Dividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292). So, 29200 \/ 73 = 400. The total number of candidates is 400.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:22:22+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":"In an examination, 25% of the candidates failed in Mathematics and 12%","description":"The correct answer is B) 400. Let M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both. Given: M = 25%, E = 12%, B = 10%. The percentage of candidates who failed in at least one subject is given by the formula: P(M U E) = P(M) + P(E) - P(M \u2229 E) Percentage failed in at least one subject = 25% + 12% - 10% = 37% - 10% = 27%. The percentage of candidates who passed in both subjects is the remaining percentage: Percentage passed in both = 100% - Percentage failed in at least one subject = 100% - 27% = 73%. We are given that 292 candidates passed in both subjects. Let T be the total number of candidates. So, 73% of T = 292 (73 \/ 100) * T = 292 T = (292 * 100) \/ 73 T = 29200 \/ 73 Dividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292). So, 29200 \/ 73 = 400. The total number of candidates is 400.","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-25-of-the-candidates-failed-in-mathematics-and-12\/","og_locale":"en_US","og_type":"article","og_title":"In an examination, 25% of the candidates failed in Mathematics and 12%","og_description":"The correct answer is B) 400. Let M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both. Given: M = 25%, E = 12%, B = 10%. The percentage of candidates who failed in at least one subject is given by the formula: P(M U E) = P(M) + P(E) - P(M \u2229 E) Percentage failed in at least one subject = 25% + 12% - 10% = 37% - 10% = 27%. The percentage of candidates who passed in both subjects is the remaining percentage: Percentage passed in both = 100% - Percentage failed in at least one subject = 100% - 27% = 73%. We are given that 292 candidates passed in both subjects. Let T be the total number of candidates. So, 73% of T = 292 (73 \/ 100) * T = 292 T = (292 * 100) \/ 73 T = 29200 \/ 73 Dividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292). So, 29200 \/ 73 = 400. The total number of candidates is 400.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:22:22+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\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/","url":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/","name":"In an examination, 25% of the candidates failed in Mathematics and 12%","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:22:22+00:00","dateModified":"2025-06-01T10:22:22+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is B) 400. Let M be the percentage of candidates who failed in Mathematics, E be the percentage who failed in English, and B be the percentage who failed in both. Given: M = 25%, E = 12%, B = 10%. The percentage of candidates who failed in at least one subject is given by the formula: P(M U E) = P(M) + P(E) - P(M \u2229 E) Percentage failed in at least one subject = 25% + 12% - 10% = 37% - 10% = 27%. The percentage of candidates who passed in both subjects is the remaining percentage: Percentage passed in both = 100% - Percentage failed in at least one subject = 100% - 27% = 73%. We are given that 292 candidates passed in both subjects. Let T be the total number of candidates. So, 73% of T = 292 (73 \/ 100) * T = 292 T = (292 * 100) \/ 73 T = 29200 \/ 73 Dividing 29200 by 73: 292 \/ 73 = 4 (since 73 * 4 = 292). So, 29200 \/ 73 = 400. The total number of candidates is 400.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/in-an-examination-25-of-the-candidates-failed-in-mathematics-and-12\/#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, 25% of the candidates failed in Mathematics and 12%"}]},{"@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\/90179","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=90179"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90179\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}