{"id":89597,"date":"2025-06-01T10:07:50","date_gmt":"2025-06-01T10:07:50","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89597"},"modified":"2025-06-01T10:07:50","modified_gmt":"2025-06-01T10:07:50","slug":"if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/","title":{"rendered":"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f"},"content":{"rendered":"<p>If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\frac{12}{13}$, then the ratio of X to Z is<\/p>\n<p>[amp_mcq option1=&#8221;$\\frac{13}{3}$&#8221; option2=&#8221;$\\frac{1}{3}$&#8221; option3=&#8221;$\\frac{4}{13}$&#8221; option4=&#8221;$\\frac{9}{13}$&#8221; correct=&#8221;option4&#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; 2013<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2013.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2013\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nThe ratio of X to Y is given as $\\frac{X}{Y} = \\frac{3}{4}$.<br \/>\nThe ratio of Y to Z is given as $\\frac{Y}{Z} = \\frac{12}{13}$.<br \/>\nTo find the ratio of X to Z ($\\frac{X}{Z}$), we can multiply the two given ratios:<br \/>\n$\\frac{X}{Y} \\times \\frac{Y}{Z} = \\frac{X}{Z}$<br \/>\nSubstituting the given values:<br \/>\n$\\frac{3}{4} \\times \\frac{12}{13} = \\frac{X}{Z}$<br \/>\n$\\frac{3 \\times 12}{4 \\times 13} = \\frac{X}{Z}$<br \/>\n$\\frac{36}{52} = \\frac{X}{Z}$<br \/>\nSimplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4:<br \/>\n$\\frac{36 \\div 4}{52 \\div 4} = \\frac{9}{13}$<br \/>\nSo, the ratio of X to Z is $\\frac{9}{13}$.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\nTo find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $\\frac{X}{Z} = \\frac{X}{Y} \\times \\frac{Y}{Z}$.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis method works for any number of intermediate ratios in a chain, e.g., if you have A:B, B:C, C:D, then A:D = (A\/B) * (B\/C) * (C\/D). It is important that the intermediate variable (Y in this case) cancels out during the multiplication.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\frac{12}{13}$, then the ratio of X to Z is [amp_mcq option1=&#8221;$\\frac{13}{3}$&#8221; option2=&#8221;$\\frac{1}{3}$&#8221; option3=&#8221;$\\frac{4}{13}$&#8221; option4=&#8221;$\\frac{9}{13}$&#8221; correct=&#8221;option4&#8243;] This question was previously asked in UPSC CAPF &#8211; 2013 Download PDFAttempt Online The ratio of X to Y is given as $\\frac{X}{Y} &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/#more-89597\">Detailed Solution<span class=\"screen-reader-text\">If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f<\/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":[1467,1102],"class_list":["post-89597","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1467","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>If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f<\/title>\n<meta name=\"description\" content=\"The ratio of X to Y is given as $frac{X}{Y} = frac{3}{4}$. The ratio of Y to Z is given as $frac{Y}{Z} = frac{12}{13}$. To find the ratio of X to Z ($frac{X}{Z}$), we can multiply the two given ratios: $frac{X}{Y} times frac{Y}{Z} = frac{X}{Z}$ Substituting the given values: $frac{3}{4} times frac{12}{13} = frac{X}{Z}$ $frac{3 times 12}{4 times 13} = frac{X}{Z}$ $frac{36}{52} = frac{X}{Z}$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4: $frac{36 div 4}{52 div 4} = frac{9}{13}$ So, the ratio of X to Z is $frac{9}{13}$. To find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $frac{X}{Z} = frac{X}{Y} times frac{Y}{Z}$.\" \/>\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\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f\" \/>\n<meta property=\"og:description\" content=\"The ratio of X to Y is given as $frac{X}{Y} = frac{3}{4}$. The ratio of Y to Z is given as $frac{Y}{Z} = frac{12}{13}$. To find the ratio of X to Z ($frac{X}{Z}$), we can multiply the two given ratios: $frac{X}{Y} times frac{Y}{Z} = frac{X}{Z}$ Substituting the given values: $frac{3}{4} times frac{12}{13} = frac{X}{Z}$ $frac{3 times 12}{4 times 13} = frac{X}{Z}$ $frac{36}{52} = frac{X}{Z}$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4: $frac{36 div 4}{52 div 4} = frac{9}{13}$ So, the ratio of X to Z is $frac{9}{13}$. To find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $frac{X}{Z} = frac{X}{Y} times frac{Y}{Z}$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:07:50+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":"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f","description":"The ratio of X to Y is given as $frac{X}{Y} = frac{3}{4}$. The ratio of Y to Z is given as $frac{Y}{Z} = frac{12}{13}$. To find the ratio of X to Z ($frac{X}{Z}$), we can multiply the two given ratios: $frac{X}{Y} times frac{Y}{Z} = frac{X}{Z}$ Substituting the given values: $frac{3}{4} times frac{12}{13} = frac{X}{Z}$ $frac{3 times 12}{4 times 13} = frac{X}{Z}$ $frac{36}{52} = frac{X}{Z}$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4: $frac{36 div 4}{52 div 4} = frac{9}{13}$ So, the ratio of X to Z is $frac{9}{13}$. To find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $frac{X}{Z} = frac{X}{Y} times frac{Y}{Z}$.","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\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/","og_locale":"en_US","og_type":"article","og_title":"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f","og_description":"The ratio of X to Y is given as $frac{X}{Y} = frac{3}{4}$. The ratio of Y to Z is given as $frac{Y}{Z} = frac{12}{13}$. To find the ratio of X to Z ($frac{X}{Z}$), we can multiply the two given ratios: $frac{X}{Y} times frac{Y}{Z} = frac{X}{Z}$ Substituting the given values: $frac{3}{4} times frac{12}{13} = frac{X}{Z}$ $frac{3 times 12}{4 times 13} = frac{X}{Z}$ $frac{36}{52} = frac{X}{Z}$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4: $frac{36 div 4}{52 div 4} = frac{9}{13}$ So, the ratio of X to Z is $frac{9}{13}$. To find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $frac{X}{Z} = frac{X}{Y} times frac{Y}{Z}$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:07:50+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\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/","name":"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:07:50+00:00","dateModified":"2025-06-01T10:07:50+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The ratio of X to Y is given as $\\frac{X}{Y} = \\frac{3}{4}$. The ratio of Y to Z is given as $\\frac{Y}{Z} = \\frac{12}{13}$. To find the ratio of X to Z ($\\frac{X}{Z}$), we can multiply the two given ratios: $\\frac{X}{Y} \\times \\frac{Y}{Z} = \\frac{X}{Z}$ Substituting the given values: $\\frac{3}{4} \\times \\frac{12}{13} = \\frac{X}{Z}$ $\\frac{3 \\times 12}{4 \\times 13} = \\frac{X}{Z}$ $\\frac{36}{52} = \\frac{X}{Z}$ Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4: $\\frac{36 \\div 4}{52 \\div 4} = \\frac{9}{13}$ So, the ratio of X to Z is $\\frac{9}{13}$. To find the ratio of X to Z given ratios of X to Y and Y to Z, the ratios can be multiplied: $\\frac{X}{Z} = \\frac{X}{Y} \\times \\frac{Y}{Z}$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-ratio-of-x-to-y-is-frac34-and-the-ratio-of-y-to-z-is-f\/#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":"If the ratio of X to Y is $\\frac{3}{4}$ and the ratio of Y to Z is $\\f"}]},{"@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\/89597","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=89597"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89597\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89597"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89597"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89597"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}