{"id":90615,"date":"2025-06-01T10:32:11","date_gmt":"2025-06-01T10:32:11","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90615"},"modified":"2025-06-01T10:32:11","modified_gmt":"2025-06-01T10:32:11","slug":"a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/","title":{"rendered":"A and B together can finish a job in 20 days. B and C together can fin"},"content":{"rendered":"

A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?<\/p>\n

[amp_mcq option1=”35 2\/7 days” option2=”37 1\/2 days” option3=”34 2\/7 days” option4=”33 2\/7 days” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nIf A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days.
\n<\/section>\n
\n– Let the amount of work done by A, B, and C in one day be a, b, and c respectively.
\n– A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day)
\n– B and C together finish the job in 30 days: b + c = 1\/30
\n– A and C together finish the job in 24 days: a + c = 1\/24
\n– Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24
\n– 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120)
\n– 2(a + b + c) = 15 \/ 120 = 1\/8
\n– a + b + c = 1\/16 (Combined work rate of A, B, and C in one day)
\n– To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate:
\n– a = (a + b + c) – (b + c)
\n– a = 1\/16 – 1\/30
\n– Find a common denominator (LCM of 16 and 30 is 240):
\n– a = (15\/240) – (8\/240) = (15 – 8) \/ 240 = 7\/240
\n– A’s work rate is 7\/240 of the job per day.
\n– The time taken by A alone to finish the job is the reciprocal of A’s work rate:
\n– Time for A = 1 \/ (7\/240) = 240 \/ 7 days.
\n– Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2.
\n– So, 240\/7 days = 34 and 2\/7 days.
\n<\/section>\n
\nSimilarly, the time taken by B or C alone can be calculated:
\nb = (a+b+c) – (a+c) = 1\/16 – 1\/24 = (3 – 2)\/48 = 1\/48. Time for B = 48 days.
\nc = (a+b+c) – (a+b) = 1\/16 – 1\/20 = (5 – 4)\/80 = 1\/80. Time for C = 80 days.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job? [amp_mcq option1=”35 2\/7 days” option2=”37 1\/2 days” option3=”34 2\/7 days” option4=”33 … <\/p>\n

Detailed SolutionA and B together can finish a job in 20 days. B and C together can fin<\/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":[1110,1102],"class_list":["post-90615","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1110","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA and B together can finish a job in 20 days. B and C together can fin<\/title>\n<meta name=\"description\" content=\"If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days. - Let the amount of work done by A, B, and C in one day be a, b, and c respectively. - A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day) - B and C together finish the job in 30 days: b + c = 1\/30 - A and C together finish the job in 24 days: a + c = 1\/24 - Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24 - 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120) - 2(a + b + c) = 15 \/ 120 = 1\/8 - a + b + c = 1\/16 (Combined work rate of A, B, and C in one day) - To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate: - a = (a + b + c) - (b + c) - a = 1\/16 - 1\/30 - Find a common denominator (LCM of 16 and 30 is 240): - a = (15\/240) - (8\/240) = (15 - 8) \/ 240 = 7\/240 - A's work rate is 7\/240 of the job per day. - The time taken by A alone to finish the job is the reciprocal of A's work rate: - Time for A = 1 \/ (7\/240) = 240 \/ 7 days. - Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2. - So, 240\/7 days = 34 and 2\/7 days.\" \/>\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\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A and B together can finish a job in 20 days. B and C together can fin\" \/>\n<meta property=\"og:description\" content=\"If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days. - Let the amount of work done by A, B, and C in one day be a, b, and c respectively. - A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day) - B and C together finish the job in 30 days: b + c = 1\/30 - A and C together finish the job in 24 days: a + c = 1\/24 - Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24 - 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120) - 2(a + b + c) = 15 \/ 120 = 1\/8 - a + b + c = 1\/16 (Combined work rate of A, B, and C in one day) - To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate: - a = (a + b + c) - (b + c) - a = 1\/16 - 1\/30 - Find a common denominator (LCM of 16 and 30 is 240): - a = (15\/240) - (8\/240) = (15 - 8) \/ 240 = 7\/240 - A's work rate is 7\/240 of the job per day. - The time taken by A alone to finish the job is the reciprocal of A's work rate: - Time for A = 1 \/ (7\/240) = 240 \/ 7 days. - Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2. - So, 240\/7 days = 34 and 2\/7 days.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:32:11+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":"A and B together can finish a job in 20 days. B and C together can fin","description":"If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days. - Let the amount of work done by A, B, and C in one day be a, b, and c respectively. - A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day) - B and C together finish the job in 30 days: b + c = 1\/30 - A and C together finish the job in 24 days: a + c = 1\/24 - Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24 - 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120) - 2(a + b + c) = 15 \/ 120 = 1\/8 - a + b + c = 1\/16 (Combined work rate of A, B, and C in one day) - To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate: - a = (a + b + c) - (b + c) - a = 1\/16 - 1\/30 - Find a common denominator (LCM of 16 and 30 is 240): - a = (15\/240) - (8\/240) = (15 - 8) \/ 240 = 7\/240 - A's work rate is 7\/240 of the job per day. - The time taken by A alone to finish the job is the reciprocal of A's work rate: - Time for A = 1 \/ (7\/240) = 240 \/ 7 days. - Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2. - So, 240\/7 days = 34 and 2\/7 days.","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\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/","og_locale":"en_US","og_type":"article","og_title":"A and B together can finish a job in 20 days. B and C together can fin","og_description":"If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days. - Let the amount of work done by A, B, and C in one day be a, b, and c respectively. - A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day) - B and C together finish the job in 30 days: b + c = 1\/30 - A and C together finish the job in 24 days: a + c = 1\/24 - Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24 - 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120) - 2(a + b + c) = 15 \/ 120 = 1\/8 - a + b + c = 1\/16 (Combined work rate of A, B, and C in one day) - To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate: - a = (a + b + c) - (b + c) - a = 1\/16 - 1\/30 - Find a common denominator (LCM of 16 and 30 is 240): - a = (15\/240) - (8\/240) = (15 - 8) \/ 240 = 7\/240 - A's work rate is 7\/240 of the job per day. - The time taken by A alone to finish the job is the reciprocal of A's work rate: - Time for A = 1 \/ (7\/240) = 240 \/ 7 days. - Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2. - So, 240\/7 days = 34 and 2\/7 days.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:32:11+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\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/","name":"A and B together can finish a job in 20 days. B and C together can fin","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:32:11+00:00","dateModified":"2025-06-01T10:32:11+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2\/7 days. - Let the amount of work done by A, B, and C in one day be a, b, and c respectively. - A and B together finish the job in 20 days: a + b = 1\/20 (Work done in one day) - B and C together finish the job in 30 days: b + c = 1\/30 - A and C together finish the job in 24 days: a + c = 1\/24 - Add the three equations: (a + b) + (b + c) + (a + c) = 1\/20 + 1\/30 + 1\/24 - 2a + 2b + 2c = (6 + 4 + 5) \/ 120 (LCM of 20, 30, 24 is 120) - 2(a + b + c) = 15 \/ 120 = 1\/8 - a + b + c = 1\/16 (Combined work rate of A, B, and C in one day) - To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate: - a = (a + b + c) - (b + c) - a = 1\/16 - 1\/30 - Find a common denominator (LCM of 16 and 30 is 240): - a = (15\/240) - (8\/240) = (15 - 8) \/ 240 = 7\/240 - A's work rate is 7\/240 of the job per day. - The time taken by A alone to finish the job is the reciprocal of A's work rate: - Time for A = 1 \/ (7\/240) = 240 \/ 7 days. - Convert the improper fraction to a mixed number: 240 \u00f7 7 = 34 with a remainder of 2. - So, 240\/7 days = 34 and 2\/7 days.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-together-can-finish-a-job-in-20-days-b-and-c-together-can-fin\/#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":"A and B together can finish a job in 20 days. B and C together can fin"}]},{"@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\/90615","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=90615"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90615\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90615"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90615"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90615"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}