{"id":89234,"date":"2025-06-01T09:59:30","date_gmt":"2025-06-01T09:59:30","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89234"},"modified":"2025-06-01T09:59:30","modified_gmt":"2025-06-01T09:59:30","slug":"the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/","title":{"rendered":"The mean age of combined group of men and women is 25 years. If the me"},"content":{"rendered":"<p>The mean age of combined group of men and women is 25 years. If the mean age of group of men is 26 and that of group of women is 21, then percentage of men and women in the group respectively is :<\/p>\n<p>[amp_mcq option1=&#8221;60, 40&#8243; option2=&#8221;80, 20&#8243; option3=&#8221;30, 70&#8243; option4=&#8221;50, 50&#8243; correct=&#8221;option2&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CAPF &#8211; 2009<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2009.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2009\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nLet M be the number of men and W be the number of women in the group.<br \/>\nThe total number of people in the group is M + W.<br \/>\nThe mean age of men is 26, so the sum of ages of men is 26M.<br \/>\nThe mean age of women is 21, so the sum of ages of women is 21W.<br \/>\nThe mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W).<\/p>\n<p>The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women.<br \/>\n26M + 21W = 25(M + W)<br \/>\n26M + 21W = 25M + 25W<br \/>\nSubtract 25M from both sides:<br \/>\n26M &#8211; 25M + 21W = 25W<br \/>\nM + 21W = 25W<br \/>\nSubtract 21W from both sides:<br \/>\nM = 25W &#8211; 21W<br \/>\nM = 4W<\/p>\n<p>The number of men is 4 times the number of women.<br \/>\nThe total number of people is M + W = 4W + W = 5W.<br \/>\nThe percentage of men in the group is (Number of men \/ Total people) * 100<br \/>\nPercentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%.<br \/>\nThe percentage of women in the group is (Number of women \/ Total people) * 100<br \/>\nPercentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%.<\/p>\n<p>The percentage of men and women in the group respectively is 80% and 20%.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nThis problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nUsing the alligation method:<br \/>\nMean age of Men (M) = 26<br \/>\nMean age of Women (W) = 21<br \/>\nMean age of Combined (C) = 25<br \/>\nAbsolute difference between M and C = |26 &#8211; 25| = 1<br \/>\nAbsolute difference between W and C = |21 &#8211; 25| = |-4| = 4<br \/>\nThe ratio of the number of Women to Men is the ratio of the differences (M-C) : (C-W) = 1 : 4.<br \/>\nSo, W : M = 1 : 4, which means M = 4W.<br \/>\nThe ratio of Men to Women is M : W = 4 : 1.<br \/>\nTotal parts = 4 + 1 = 5.<br \/>\nPercentage of Men = (4\/5) * 100 = 80%.<br \/>\nPercentage of Women = (1\/5) * 100 = 20%.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The mean age of combined group of men and women is 25 years. If the mean age of group of men is 26 and that of group of women is 21, then percentage of men and women in the group respectively is : [amp_mcq option1=&#8221;60, 40&#8243; option2=&#8221;80, 20&#8243; option3=&#8221;30, 70&#8243; option4=&#8221;50, 50&#8243; correct=&#8221;option2&#8243;] This question &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"The mean age of combined group of men and women is 25 years. If the me\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/#more-89234\">Detailed Solution<span class=\"screen-reader-text\">The mean age of combined group of men and women is 25 years. If the me<\/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":[1462,1102],"class_list":["post-89234","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1462","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The mean age of combined group of men and women is 25 years. If the me<\/title>\n<meta name=\"description\" content=\"Let M be the number of men and W be the number of women in the group. The total number of people in the group is M + W. The mean age of men is 26, so the sum of ages of men is 26M. The mean age of women is 21, so the sum of ages of women is 21W. The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W). The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women. 26M + 21W = 25(M + W) 26M + 21W = 25M + 25W Subtract 25M from both sides: 26M - 25M + 21W = 25W M + 21W = 25W Subtract 21W from both sides: M = 25W - 21W M = 4W The number of men is 4 times the number of women. The total number of people is M + W = 4W + W = 5W. The percentage of men in the group is (Number of men \/ Total people) * 100 Percentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%. The percentage of women in the group is (Number of women \/ Total people) * 100 Percentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%. The percentage of men and women in the group respectively is 80% and 20%. This problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.\" \/>\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\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The mean age of combined group of men and women is 25 years. If the me\" \/>\n<meta property=\"og:description\" content=\"Let M be the number of men and W be the number of women in the group. The total number of people in the group is M + W. The mean age of men is 26, so the sum of ages of men is 26M. The mean age of women is 21, so the sum of ages of women is 21W. The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W). The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women. 26M + 21W = 25(M + W) 26M + 21W = 25M + 25W Subtract 25M from both sides: 26M - 25M + 21W = 25W M + 21W = 25W Subtract 21W from both sides: M = 25W - 21W M = 4W The number of men is 4 times the number of women. The total number of people is M + W = 4W + W = 5W. The percentage of men in the group is (Number of men \/ Total people) * 100 Percentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%. The percentage of women in the group is (Number of women \/ Total people) * 100 Percentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%. The percentage of men and women in the group respectively is 80% and 20%. This problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T09:59:30+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":"The mean age of combined group of men and women is 25 years. If the me","description":"Let M be the number of men and W be the number of women in the group. The total number of people in the group is M + W. The mean age of men is 26, so the sum of ages of men is 26M. The mean age of women is 21, so the sum of ages of women is 21W. The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W). The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women. 26M + 21W = 25(M + W) 26M + 21W = 25M + 25W Subtract 25M from both sides: 26M - 25M + 21W = 25W M + 21W = 25W Subtract 21W from both sides: M = 25W - 21W M = 4W The number of men is 4 times the number of women. The total number of people is M + W = 4W + W = 5W. The percentage of men in the group is (Number of men \/ Total people) * 100 Percentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%. The percentage of women in the group is (Number of women \/ Total people) * 100 Percentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%. The percentage of men and women in the group respectively is 80% and 20%. This problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.","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\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/","og_locale":"en_US","og_type":"article","og_title":"The mean age of combined group of men and women is 25 years. If the me","og_description":"Let M be the number of men and W be the number of women in the group. The total number of people in the group is M + W. The mean age of men is 26, so the sum of ages of men is 26M. The mean age of women is 21, so the sum of ages of women is 21W. The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W). The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women. 26M + 21W = 25(M + W) 26M + 21W = 25M + 25W Subtract 25M from both sides: 26M - 25M + 21W = 25W M + 21W = 25W Subtract 21W from both sides: M = 25W - 21W M = 4W The number of men is 4 times the number of women. The total number of people is M + W = 4W + W = 5W. The percentage of men in the group is (Number of men \/ Total people) * 100 Percentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%. The percentage of women in the group is (Number of women \/ Total people) * 100 Percentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%. The percentage of men and women in the group respectively is 80% and 20%. This problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T09:59:30+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\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/","name":"The mean age of combined group of men and women is 25 years. If the me","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T09:59:30+00:00","dateModified":"2025-06-01T09:59:30+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let M be the number of men and W be the number of women in the group. The total number of people in the group is M + W. The mean age of men is 26, so the sum of ages of men is 26M. The mean age of women is 21, so the sum of ages of women is 21W. The mean age of the combined group is 25. The sum of ages of the combined group is 25(M + W). The sum of ages of men and women combined is the sum of ages of men plus the sum of ages of women. 26M + 21W = 25(M + W) 26M + 21W = 25M + 25W Subtract 25M from both sides: 26M - 25M + 21W = 25W M + 21W = 25W Subtract 21W from both sides: M = 25W - 21W M = 4W The number of men is 4 times the number of women. The total number of people is M + W = 4W + W = 5W. The percentage of men in the group is (Number of men \/ Total people) * 100 Percentage of men = (4W \/ 5W) * 100 = (4\/5) * 100 = 80%. The percentage of women in the group is (Number of women \/ Total people) * 100 Percentage of women = (W \/ 5W) * 100 = (1\/5) * 100 = 20%. The percentage of men and women in the group respectively is 80% and 20%. This problem involves weighted averages. The overall mean is a weighted average of the group means, where the weights are the proportions of each group in the total. Setting up the equation based on the sum of ages is a standard method. The alligation method provides a quicker way to find the ratio of the quantities based on the differences between the group means and the overall mean.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-mean-age-of-combined-group-of-men-and-women-is-25-years-if-the-me\/#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":"The mean age of combined group of men and women is 25 years. If the me"}]},{"@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\/89234","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=89234"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89234\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89234"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89234"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}