{"id":90565,"date":"2025-06-01T10:31:07","date_gmt":"2025-06-01T10:31:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90565"},"modified":"2025-06-01T10:31:07","modified_gmt":"2025-06-01T10:31:07","slug":"two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/","title":{"rendered":"Two years ago, the age of A was three times the age of B. If B is curr"},"content":{"rendered":"

Two years ago, the age of A was three times the age of B. If B is currently 9 years old, then after how many years, the age of A will be double of the age of B ?<\/p>\n

[amp_mcq option1=”2 years” option2=”3 years” option3=”4 years” option4=”5 years” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2020<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet A be A’s current age and B be B’s current age.
\nWe are given that B’s current age is 9 years, so B = 9.
\nTwo years ago:
\nA’s age was A – 2.
\nB’s age was B – 2 = 9 – 2 = 7.
\nAccording to the problem, two years ago, the age of A was three times the age of B:
\nA – 2 = 3 * (B – 2)
\nA – 2 = 3 * 7
\nA – 2 = 21
\nA = 21 + 2 = 23.
\nSo, A’s current age is 23 years.
\nWe want to find the number of years (let’s call it x) after which A’s age will be double B’s age.
\nAfter x years:
\nA’s age will be A + x = 23 + x.
\nB’s age will be B + x = 9 + x.
\nWe are given that after x years, A’s age will be double B’s age:
\n23 + x = 2 * (9 + x)
\n23 + x = 18 + 2x
\nSubtract x from both sides:
\n23 = 18 + 2x – x
\n23 = 18 + x
\nSubtract 18 from both sides:
\nx = 23 – 18
\nx = 5.
\nSo, after 5 years, the age of A will be double the age of B.
\n<\/section>\n
\n– Set up variables for the current ages.
\n– Translate the information about past ages into equations based on the current age variables.
\n– Solve for the unknown current age(s).
\n– Set up equations for future ages based on adding an unknown number of years (x).
\n– Solve for x based on the given relationship between future ages.
\n<\/section>\n
\nAlways verify the answer by plugging the calculated number of years back into the future age condition. After 5 years, A will be 23 + 5 = 28, and B will be 9 + 5 = 14. Since 28 = 2 * 14, the condition is met.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Two years ago, the age of A was three times the age of B. If B is currently 9 years old, then after how many years, the age of A will be double of the age of B ? [amp_mcq option1=”2 years” option2=”3 years” option3=”4 years” option4=”5 years” correct=”option4″] This question was previously asked in … <\/p>\n

Detailed SolutionTwo years ago, the age of A was three times the age of B. If B is curr<\/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":[1288,1102],"class_list":["post-90565","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1288","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nTwo years ago, the age of A was three times the age of B. If B is curr<\/title>\n<meta name=\"description\" content=\"Let A be A's current age and B be B's current age. We are given that B's current age is 9 years, so B = 9. Two years ago: A's age was A - 2. B's age was B - 2 = 9 - 2 = 7. According to the problem, two years ago, the age of A was three times the age of B: A - 2 = 3 * (B - 2) A - 2 = 3 * 7 A - 2 = 21 A = 21 + 2 = 23. So, A's current age is 23 years. We want to find the number of years (let's call it x) after which A's age will be double B's age. After x years: A's age will be A + x = 23 + x. B's age will be B + x = 9 + x. We are given that after x years, A's age will be double B's age: 23 + x = 2 * (9 + x) 23 + x = 18 + 2x Subtract x from both sides: 23 = 18 + 2x - x 23 = 18 + x Subtract 18 from both sides: x = 23 - 18 x = 5. So, after 5 years, the age of A will be double the age of B. - Set up variables for the current ages. - Translate the information about past ages into equations based on the current age variables. - Solve for the unknown current age(s). - Set up equations for future ages based on adding an unknown number of years (x). - Solve for x based on the given relationship between future ages.\" \/>\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\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Two years ago, the age of A was three times the age of B. If B is curr\" \/>\n<meta property=\"og:description\" content=\"Let A be A's current age and B be B's current age. We are given that B's current age is 9 years, so B = 9. Two years ago: A's age was A - 2. B's age was B - 2 = 9 - 2 = 7. According to the problem, two years ago, the age of A was three times the age of B: A - 2 = 3 * (B - 2) A - 2 = 3 * 7 A - 2 = 21 A = 21 + 2 = 23. So, A's current age is 23 years. We want to find the number of years (let's call it x) after which A's age will be double B's age. After x years: A's age will be A + x = 23 + x. B's age will be B + x = 9 + x. We are given that after x years, A's age will be double B's age: 23 + x = 2 * (9 + x) 23 + x = 18 + 2x Subtract x from both sides: 23 = 18 + 2x - x 23 = 18 + x Subtract 18 from both sides: x = 23 - 18 x = 5. So, after 5 years, the age of A will be double the age of B. - Set up variables for the current ages. - Translate the information about past ages into equations based on the current age variables. - Solve for the unknown current age(s). - Set up equations for future ages based on adding an unknown number of years (x). - Solve for x based on the given relationship between future ages.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:31:07+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":"Two years ago, the age of A was three times the age of B. If B is curr","description":"Let A be A's current age and B be B's current age. We are given that B's current age is 9 years, so B = 9. Two years ago: A's age was A - 2. B's age was B - 2 = 9 - 2 = 7. According to the problem, two years ago, the age of A was three times the age of B: A - 2 = 3 * (B - 2) A - 2 = 3 * 7 A - 2 = 21 A = 21 + 2 = 23. So, A's current age is 23 years. We want to find the number of years (let's call it x) after which A's age will be double B's age. After x years: A's age will be A + x = 23 + x. B's age will be B + x = 9 + x. We are given that after x years, A's age will be double B's age: 23 + x = 2 * (9 + x) 23 + x = 18 + 2x Subtract x from both sides: 23 = 18 + 2x - x 23 = 18 + x Subtract 18 from both sides: x = 23 - 18 x = 5. So, after 5 years, the age of A will be double the age of B. - Set up variables for the current ages. - Translate the information about past ages into equations based on the current age variables. - Solve for the unknown current age(s). - Set up equations for future ages based on adding an unknown number of years (x). - Solve for x based on the given relationship between future ages.","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\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/","og_locale":"en_US","og_type":"article","og_title":"Two years ago, the age of A was three times the age of B. If B is curr","og_description":"Let A be A's current age and B be B's current age. We are given that B's current age is 9 years, so B = 9. Two years ago: A's age was A - 2. B's age was B - 2 = 9 - 2 = 7. According to the problem, two years ago, the age of A was three times the age of B: A - 2 = 3 * (B - 2) A - 2 = 3 * 7 A - 2 = 21 A = 21 + 2 = 23. So, A's current age is 23 years. We want to find the number of years (let's call it x) after which A's age will be double B's age. After x years: A's age will be A + x = 23 + x. B's age will be B + x = 9 + x. We are given that after x years, A's age will be double B's age: 23 + x = 2 * (9 + x) 23 + x = 18 + 2x Subtract x from both sides: 23 = 18 + 2x - x 23 = 18 + x Subtract 18 from both sides: x = 23 - 18 x = 5. So, after 5 years, the age of A will be double the age of B. - Set up variables for the current ages. - Translate the information about past ages into equations based on the current age variables. - Solve for the unknown current age(s). - Set up equations for future ages based on adding an unknown number of years (x). - Solve for x based on the given relationship between future ages.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:31:07+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\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/","url":"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/","name":"Two years ago, the age of A was three times the age of B. If B is curr","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:31:07+00:00","dateModified":"2025-06-01T10:31:07+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let A be A's current age and B be B's current age. We are given that B's current age is 9 years, so B = 9. Two years ago: A's age was A - 2. B's age was B - 2 = 9 - 2 = 7. According to the problem, two years ago, the age of A was three times the age of B: A - 2 = 3 * (B - 2) A - 2 = 3 * 7 A - 2 = 21 A = 21 + 2 = 23. So, A's current age is 23 years. We want to find the number of years (let's call it x) after which A's age will be double B's age. After x years: A's age will be A + x = 23 + x. B's age will be B + x = 9 + x. We are given that after x years, A's age will be double B's age: 23 + x = 2 * (9 + x) 23 + x = 18 + 2x Subtract x from both sides: 23 = 18 + 2x - x 23 = 18 + x Subtract 18 from both sides: x = 23 - 18 x = 5. So, after 5 years, the age of A will be double the age of B. - Set up variables for the current ages. - Translate the information about past ages into equations based on the current age variables. - Solve for the unknown current age(s). - Set up equations for future ages based on adding an unknown number of years (x). - Solve for x based on the given relationship between future ages.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/two-years-ago-the-age-of-a-was-three-times-the-age-of-b-if-b-is-curr\/#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":"Two years ago, the age of A was three times the age of B. If B is curr"}]},{"@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\/90565","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=90565"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90565\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90565"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90565"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90565"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}