{"id":90970,"date":"2025-06-01T10:42:14","date_gmt":"2025-06-01T10:42:14","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90970"},"modified":"2025-06-01T10:42:14","modified_gmt":"2025-06-01T10:42:14","slug":"the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/","title":{"rendered":"The ratio of present ages (in years) of X to Y is equal to the ratio o"},"content":{"rendered":"

The ratio of present ages (in years) of X to Y is equal to the ratio of present ages (in years) of Y to Z. If the present age of Y is 15 years, then which of the following can be the sum of the ages (in years) of X, Y and Z ?<\/p>\n

[amp_mcq option1=”35″ option2=”40″ option3=”49″ option4=”55″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is C) 49.
\n<\/section>\n
\nLet the present ages of X, Y, and Z be $X, Y, Z$ years respectively.
\nThe ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z.
\n$\\frac{X}{Y} = \\frac{Y}{Z}$
\nThis implies $Y^2 = XZ$.
\nGiven that the present age of Y is 15 years, so $Y=15$.
\n$15^2 = XZ \\implies 225 = XZ$.
\nWe are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. We need to find integer pairs $(X, Z)$ whose product is 225 and check the sum $X+15+Z$ against the options.
\n<\/section>\n
\nWe list integer factors of 225 and form pairs $(X, Z)$ such that $XZ=225$. We can assume $X \\le Z$ without loss of generality, as the sum $X+15+Z$ will be the same for $(X,Z)$ and $(Z,X)$.
\nFactors of $225 = 3^2 \\times 5^2$: 1, 3, 5, 9, 15, 25, 45, 75, 225.
\nPossible pairs $(X, Z)$ with $X \\le Z$ and $XZ=225$:
\n– $(1, 225) \\implies X+15+Z = 1 + 15 + 225 = 241$. Not an option.
\n– $(3, 75) \\implies X+15+Z = 3 + 15 + 75 = 93$. Not an option.
\n– $(5, 45) \\implies X+15+Z = 5 + 15 + 45 = 65$. Not an option.
\n– $(9, 25) \\implies X+15+Z = 9 + 15 + 25 = 49$. This is option C.
\n– $(15, 15) \\implies X+15+Z = 15 + 15 + 15 = 45$. Not an option. (Note: this case means X=Y=Z=15, which satisfies the ratio condition, although ages are usually assumed different in such problems unless stated).<\/p>\n

Since 49 is one of the calculated possible sums (when ages are 9, 15, and 25), it is a valid answer.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The ratio of present ages (in years) of X to Y is equal to the ratio of present ages (in years) of Y to Z. If the present age of Y is 15 years, then which of the following can be the sum of the ages (in years) of X, Y and Z ? [amp_mcq … <\/p>\n

Detailed SolutionThe ratio of present ages (in years) of X to Y is equal to the ratio o<\/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":[1103,1102],"class_list":["post-90970","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe ratio of present ages (in years) of X to Y is equal to the ratio o<\/title>\n<meta name=\"description\" content=\"The correct answer is C) 49. Let the present ages of X, Y, and Z be $X, Y, Z$ years respectively. The ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z. $frac{X}{Y} = frac{Y}{Z}$ This implies $Y^2 = XZ$. Given that the present age of Y is 15 years, so $Y=15$. $15^2 = XZ implies 225 = XZ$. We are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. We need to find integer pairs $(X, Z)$ whose product is 225 and check the sum $X+15+Z$ against the options.\" \/>\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-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The ratio of present ages (in years) of X to Y is equal to the ratio o\" \/>\n<meta property=\"og:description\" content=\"The correct answer is C) 49. Let the present ages of X, Y, and Z be $X, Y, Z$ years respectively. The ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z. $frac{X}{Y} = frac{Y}{Z}$ This implies $Y^2 = XZ$. Given that the present age of Y is 15 years, so $Y=15$. $15^2 = XZ implies 225 = XZ$. We are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. We need to find integer pairs $(X, Z)$ whose product is 225 and check the sum $X+15+Z$ against the options.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:42:14+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":"The ratio of present ages (in years) of X to Y is equal to the ratio o","description":"The correct answer is C) 49. Let the present ages of X, Y, and Z be $X, Y, Z$ years respectively. The ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z. $frac{X}{Y} = frac{Y}{Z}$ This implies $Y^2 = XZ$. Given that the present age of Y is 15 years, so $Y=15$. $15^2 = XZ implies 225 = XZ$. We are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. We need to find integer pairs $(X, Z)$ whose product is 225 and check the sum $X+15+Z$ against the options.","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-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/","og_locale":"en_US","og_type":"article","og_title":"The ratio of present ages (in years) of X to Y is equal to the ratio o","og_description":"The correct answer is C) 49. Let the present ages of X, Y, and Z be $X, Y, Z$ years respectively. The ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z. $frac{X}{Y} = frac{Y}{Z}$ This implies $Y^2 = XZ$. Given that the present age of Y is 15 years, so $Y=15$. $15^2 = XZ implies 225 = XZ$. We are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. We need to find integer pairs $(X, Z)$ whose product is 225 and check the sum $X+15+Z$ against the options.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:42:14+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\/the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-present-ages-in-years-of-x-to-y-is-equal-to-the-ratio-o\/","name":"The ratio of present ages (in years) of X to Y is equal to the ratio o","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:42:14+00:00","dateModified":"2025-06-01T10:42:14+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is C) 49. Let the present ages of X, Y, and Z be $X, Y, Z$ years respectively. The ratio of present ages of X to Y is equal to the ratio of present ages of Y to Z. $\\frac{X}{Y} = \\frac{Y}{Z}$ This implies $Y^2 = XZ$. Given that the present age of Y is 15 years, so $Y=15$. $15^2 = XZ \\implies 225 = XZ$. We are looking for a possible sum of the ages $X+Y+Z = X+15+Z$. 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