{"id":89956,"date":"2025-06-01T10:17:55","date_gmt":"2025-06-01T10:17:55","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89956"},"modified":"2025-06-01T10:17:55","modified_gmt":"2025-06-01T10:17:55","slug":"the-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/","title":{"rendered":"The age of ‘E’ is twice the age of ‘S’. To find out the difference in"},"content":{"rendered":"

The age of ‘E’ is twice the age of ‘S’. To find out the difference in their ages, which of the following information is\/are sufficient ?
\nI. After five years, the ratio of their ages would be 9 : 5
\nII. Before ten years, the ratio of their ages was 3 : 1<\/p>\n

[amp_mcq option1=”Only I” option2=”Only II” option3=”Either I or II” option4=”Both I and II” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2015<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet E be the current age of E and S be the current age of S.
\nGiven: E = 2S. We need to find the difference E – S.
\nStatement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient.
\nStatement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient.
\nSince either statement alone provides enough information to find the difference in their ages, the answer is C.
\n<\/section>\n
\nThe question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. We need to check if this system of equations allows us to find the specific ages or their difference.
\n<\/section>\n
\nFrom Statement I: 5(2S+5) = 9(S+5) => 10S + 25 = 9S + 45 => S = 20. E = 2*20 = 40. Difference = 20.
\nFrom Statement II: (2S-10) = 3(S-10) => 2S – 10 = 3S – 30 => S = 20. E = 2*20 = 40. Difference = 20.
\nBoth statements lead to the same ages and difference, confirming that each is independently sufficient.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The age of ‘E’ is twice the age of ‘S’. To find out the difference in their ages, which of the following information is\/are sufficient ? I. After five years, the ratio of their ages would be 9 : 5 II. Before ten years, the ratio of their ages was 3 : 1 [amp_mcq option1=”Only … <\/p>\n

Detailed SolutionThe age of ‘E’ is twice the age of ‘S’. To find out the difference in<\/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":[1443,1102],"class_list":["post-89956","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1443","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe age of 'E' is twice the age of 'S'. To find out the difference in<\/title>\n<meta name=\"description\" content=\"Let E be the current age of E and S be the current age of S. Given: E = 2S. We need to find the difference E - S. Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient. Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient. Since either statement alone provides enough information to find the difference in their ages, the answer is C. The question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. We need to check if this system of equations allows us to find the specific ages or their difference.\" \/>\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-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The age of 'E' is twice the age of 'S'. To find out the difference in\" \/>\n<meta property=\"og:description\" content=\"Let E be the current age of E and S be the current age of S. Given: E = 2S. We need to find the difference E - S. Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient. Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient. Since either statement alone provides enough information to find the difference in their ages, the answer is C. The question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. We need to check if this system of equations allows us to find the specific ages or their difference.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:17:55+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 age of 'E' is twice the age of 'S'. To find out the difference in","description":"Let E be the current age of E and S be the current age of S. Given: E = 2S. We need to find the difference E - S. Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient. Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient. Since either statement alone provides enough information to find the difference in their ages, the answer is C. The question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. We need to check if this system of equations allows us to find the specific ages or their difference.","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-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/","og_locale":"en_US","og_type":"article","og_title":"The age of 'E' is twice the age of 'S'. To find out the difference in","og_description":"Let E be the current age of E and S be the current age of S. Given: E = 2S. We need to find the difference E - S. Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient. Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient. Since either statement alone provides enough information to find the difference in their ages, the answer is C. The question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. We need to check if this system of equations allows us to find the specific ages or their difference.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:17:55+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-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-age-of-e-is-twice-the-age-of-s-to-find-out-the-difference-in\/","name":"The age of 'E' is twice the age of 'S'. To find out the difference in","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:17:55+00:00","dateModified":"2025-06-01T10:17:55+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let E be the current age of E and S be the current age of S. Given: E = 2S. We need to find the difference E - S. Statement I: After five years, the ratio of their ages is 9:5. So, (E+5)\/(S+5) = 9\/5. Substituting E=2S, we get (2S+5)\/(S+5) = 9\/5. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement I alone is sufficient. Statement II: Before ten years, the ratio of their ages was 3:1. So, (E-10)\/(S-10) = 3\/1. Substituting E=2S, we get (2S-10)\/(S-10) = 3\/1. This is a linear equation in S, which can be solved to find a unique value for S. Since S can be determined, E can also be determined, and thus the difference E-S can be found. So, Statement II alone is sufficient. Since either statement alone provides enough information to find the difference in their ages, the answer is C. The question asks whether the given information is sufficient to find the difference in ages. We are given a relationship between their current ages. Each statement provides an additional relationship at a different point in time. 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