{"id":90405,"date":"2025-06-01T10:27:52","date_gmt":"2025-06-01T10:27:52","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90405"},"modified":"2025-06-01T10:27:52","modified_gmt":"2025-06-01T10:27:52","slug":"if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/","title":{"rendered":"If the numerator of a fraction is increased by 200% and the denodminat"},"content":{"rendered":"

If the numerator of a fraction is increased by 200% and the denodminator is increased by 300%, the resultant fraction is 9\/17. What was the original fraction ?<\/p>\n

[amp_mcq option1=”10\/17″ option2=”11\/17″ option3=”12\/17″ option4=”13\/17″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet the original fraction be represented as n\/d, where n is the numerator and d is the denominator.
\nThe numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator.
\nNew numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n.
\nThe denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator.
\nNew denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d.
\nThe resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d).
\nWe are given that the resultant fraction is 9\/17.
\nSo, (3n) \/ (4d) = 9\/17.
\nWe need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d:
\n(3\/4) * (n\/d) = 9\/17
\nMultiply both sides by the reciprocal of (3\/4), which is (4\/3):
\nn\/d = (9\/17) * (4\/3)
\nn\/d = (9 * 4) \/ (17 * 3)
\nn\/d = 36 \/ 51
\nThis fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3.
\n36 \/ 3 = 12
\n51 \/ 3 = 17
\nSo, the original fraction was 12\/17.
\n<\/section>\n
\nWhen a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.
\n<\/section>\n
\nAlgebraic representation of word problems is key. Setting up the equation correctly based on the given percentages and the resulting fraction allows one to solve for the unknown original fraction. Simplifying the final fraction to its lowest terms is standard practice.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

If the numerator of a fraction is increased by 200% and the denodminator is increased by 300%, the resultant fraction is 9\/17. What was the original fraction ? [amp_mcq option1=”10\/17″ option2=”11\/17″ option3=”12\/17″ option4=”13\/17″ correct=”option3″] This question was previously asked in UPSC CAPF – 2019 Download PDFAttempt Online Let the original fraction be represented as n\/d, … <\/p>\n

Detailed SolutionIf the numerator of a fraction is increased by 200% and the denodminat<\/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":[1119,1102],"class_list":["post-90405","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1119","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIf the numerator of a fraction is increased by 200% and the denodminat<\/title>\n<meta name=\"description\" content=\"Let the original fraction be represented as n\/d, where n is the numerator and d is the denominator. The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator. New numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n. The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator. New denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d. The resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d). We are given that the resultant fraction is 9\/17. So, (3n) \/ (4d) = 9\/17. We need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d: (3\/4) * (n\/d) = 9\/17 Multiply both sides by the reciprocal of (3\/4), which is (4\/3): n\/d = (9\/17) * (4\/3) n\/d = (9 * 4) \/ (17 * 3) n\/d = 36 \/ 51 This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 \/ 3 = 12 51 \/ 3 = 17 So, the original fraction was 12\/17. When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.\" \/>\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-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If the numerator of a fraction is increased by 200% and the denodminat\" \/>\n<meta property=\"og:description\" content=\"Let the original fraction be represented as n\/d, where n is the numerator and d is the denominator. The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator. New numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n. The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator. New denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d. The resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d). We are given that the resultant fraction is 9\/17. So, (3n) \/ (4d) = 9\/17. We need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d: (3\/4) * (n\/d) = 9\/17 Multiply both sides by the reciprocal of (3\/4), which is (4\/3): n\/d = (9\/17) * (4\/3) n\/d = (9 * 4) \/ (17 * 3) n\/d = 36 \/ 51 This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 \/ 3 = 12 51 \/ 3 = 17 So, the original fraction was 12\/17. When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:27:52+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 numerator of a fraction is increased by 200% and the denodminat","description":"Let the original fraction be represented as n\/d, where n is the numerator and d is the denominator. The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator. New numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n. The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator. New denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d. The resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d). We are given that the resultant fraction is 9\/17. So, (3n) \/ (4d) = 9\/17. We need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d: (3\/4) * (n\/d) = 9\/17 Multiply both sides by the reciprocal of (3\/4), which is (4\/3): n\/d = (9\/17) * (4\/3) n\/d = (9 * 4) \/ (17 * 3) n\/d = 36 \/ 51 This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 \/ 3 = 12 51 \/ 3 = 17 So, the original fraction was 12\/17. When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.","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-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/","og_locale":"en_US","og_type":"article","og_title":"If the numerator of a fraction is increased by 200% and the denodminat","og_description":"Let the original fraction be represented as n\/d, where n is the numerator and d is the denominator. The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator. New numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n. The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator. New denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d. The resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d). We are given that the resultant fraction is 9\/17. So, (3n) \/ (4d) = 9\/17. We need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d: (3\/4) * (n\/d) = 9\/17 Multiply both sides by the reciprocal of (3\/4), which is (4\/3): n\/d = (9\/17) * (4\/3) n\/d = (9 * 4) \/ (17 * 3) n\/d = 36 \/ 51 This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 \/ 3 = 12 51 \/ 3 = 17 So, the original fraction was 12\/17. When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:27:52+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-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/","url":"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/","name":"If the numerator of a fraction is increased by 200% and the denodminat","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:27:52+00:00","dateModified":"2025-06-01T10:27:52+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the original fraction be represented as n\/d, where n is the numerator and d is the denominator. The numerator is increased by 200%. This means the new numerator is the original numerator plus 200% of the original numerator. New numerator = n + 200% of n = n + (200\/100) * n = n + 2n = 3n. The denominator is increased by 300%. This means the new denominator is the original denominator plus 300% of the original denominator. New denominator = d + 300% of d = d + (300\/100) * d = d + 3d = 4d. The resultant fraction is the new numerator divided by the new denominator: (3n) \/ (4d). We are given that the resultant fraction is 9\/17. So, (3n) \/ (4d) = 9\/17. We need to find the original fraction n\/d. We can rearrange the equation to solve for n\/d: (3\/4) * (n\/d) = 9\/17 Multiply both sides by the reciprocal of (3\/4), which is (4\/3): n\/d = (9\/17) * (4\/3) n\/d = (9 * 4) \/ (17 * 3) n\/d = 36 \/ 51 This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3. 36 \/ 3 = 12 51 \/ 3 = 17 So, the original fraction was 12\/17. When a quantity is increased by X%, the new quantity is the original quantity plus X% of the original quantity, which is equivalent to Original Quantity * (1 + X\/100). In this case, a 200% increase means the new value is (1 + 200\/100) = 3 times the original. A 300% increase means the new value is (1 + 300\/100) = 4 times the original.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/if-the-numerator-of-a-fraction-is-increased-by-200-and-the-denodminat\/#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 numerator of a fraction is increased by 200% and the denodminat"}]},{"@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\/90405","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=90405"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90405\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90405"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90405"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90405"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}