{"id":90844,"date":"2025-06-01T10:38:49","date_gmt":"2025-06-01T10:38:49","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90844"},"modified":"2025-06-01T10:38:49","modified_gmt":"2025-06-01T10:38:49","slug":"suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/","title":{"rendered":"Suppose A, B and C are three taps fixed to the bottom of a tank with d"},"content":{"rendered":"

Suppose A, B and C are three taps fixed to the bottom of a tank with draining capacity 1 : 2 : 3. When all three of them are on, it takes 1 hour to drain out the full tank. If A and C are on but B is off, then how much time, in minutes, will it take to empty out a full tank of water ?<\/p>\n

[amp_mcq option1=”75″ option2=”90″ option3=”105″ option4=”120″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct option is B) 90.
\n<\/section>\n
\nLet the volume of the tank be V.
\nLet the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively.
\nThe ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k.<\/p>\n

When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k.
\nIt takes 1 hour (60 minutes) to drain the full tank.
\nSo, V = (Total Rate) * Time = (6k) * 60 = 360k.<\/p>\n

When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k.
\nLet T be the time in minutes it takes to empty the full tank with A and C on.
\nThe volume drained is V.
\nV = (Rate A+C) * T = (4k) * T.<\/p>\n

We know V = 360k.
\nSo, 360k = 4k * T.
\nDivide both sides by 4k (assuming k > 0):
\nT = 360k \/ 4k = 360 \/ 4 = 90 minutes.
\n<\/section>\n

\nThis problem assumes the rates are constant and additive. The unit of rate (k) cancels out in the calculation of time. The key is setting up the relationship between volume, rate, and time (Volume = Rate \u00d7 Time) and using the given information about the ratio of rates and the time taken when all taps are open.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose A, B and C are three taps fixed to the bottom of a tank with draining capacity 1 : 2 : 3. When all three of them are on, it takes 1 hour to drain out the full tank. If A and C are on but B is off, then how much time, in … <\/p>\n

Detailed SolutionSuppose A, B and C are three taps fixed to the bottom of a tank with d<\/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":[1105,1102],"class_list":["post-90844","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nSuppose A, B and C are three taps fixed to the bottom of a tank with d<\/title>\n<meta name=\"description\" content=\"The correct option is B) 90. Let the volume of the tank be V. Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively. The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k. When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k. It takes 1 hour (60 minutes) to drain the full tank. So, V = (Total Rate) * Time = (6k) * 60 = 360k. When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k. Let T be the time in minutes it takes to empty the full tank with A and C on. The volume drained is V. V = (Rate A+C) * T = (4k) * T. We know V = 360k. So, 360k = 4k * T. Divide both sides by 4k (assuming k > 0): T = 360k \/ 4k = 360 \/ 4 = 90 minutes.\" \/>\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\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose A, B and C are three taps fixed to the bottom of a tank with d\" \/>\n<meta property=\"og:description\" content=\"The correct option is B) 90. Let the volume of the tank be V. Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively. The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k. When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k. It takes 1 hour (60 minutes) to drain the full tank. So, V = (Total Rate) * Time = (6k) * 60 = 360k. When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k. Let T be the time in minutes it takes to empty the full tank with A and C on. The volume drained is V. V = (Rate A+C) * T = (4k) * T. We know V = 360k. So, 360k = 4k * T. Divide both sides by 4k (assuming k > 0): T = 360k \/ 4k = 360 \/ 4 = 90 minutes.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:38:49+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":"Suppose A, B and C are three taps fixed to the bottom of a tank with d","description":"The correct option is B) 90. Let the volume of the tank be V. Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively. The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k. When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k. It takes 1 hour (60 minutes) to drain the full tank. So, V = (Total Rate) * Time = (6k) * 60 = 360k. When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k. Let T be the time in minutes it takes to empty the full tank with A and C on. The volume drained is V. V = (Rate A+C) * T = (4k) * T. We know V = 360k. So, 360k = 4k * T. Divide both sides by 4k (assuming k > 0): T = 360k \/ 4k = 360 \/ 4 = 90 minutes.","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\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/","og_locale":"en_US","og_type":"article","og_title":"Suppose A, B and C are three taps fixed to the bottom of a tank with d","og_description":"The correct option is B) 90. Let the volume of the tank be V. Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively. The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k. When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k. It takes 1 hour (60 minutes) to drain the full tank. So, V = (Total Rate) * Time = (6k) * 60 = 360k. When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k. Let T be the time in minutes it takes to empty the full tank with A and C on. The volume drained is V. V = (Rate A+C) * T = (4k) * T. We know V = 360k. So, 360k = 4k * T. Divide both sides by 4k (assuming k > 0): T = 360k \/ 4k = 360 \/ 4 = 90 minutes.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:38:49+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\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/","name":"Suppose A, B and C are three taps fixed to the bottom of a tank with d","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:38:49+00:00","dateModified":"2025-06-01T10:38:49+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct option is B) 90. Let the volume of the tank be V. Let the draining capacities (rates) of taps A, B, and C be R_A, R_B, and R_C respectively. The ratio of capacities is 1:2:3, so we can write R_A = k, R_B = 2k, and R_C = 3k for some constant k. When all three taps are on, the total draining rate is R_A + R_B + R_C = k + 2k + 3k = 6k. It takes 1 hour (60 minutes) to drain the full tank. So, V = (Total Rate) * Time = (6k) * 60 = 360k. When taps A and C are on, and B is off, the total draining rate is R_A + R_C = k + 3k = 4k. Let T be the time in minutes it takes to empty the full tank with A and C on. The volume drained is V. V = (Rate A+C) * T = (4k) * T. We know V = 360k. So, 360k = 4k * T. Divide both sides by 4k (assuming k > 0): T = 360k \/ 4k = 360 \/ 4 = 90 minutes.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-b-and-c-are-three-taps-fixed-to-the-bottom-of-a-tank-with-d\/#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":"Suppose A, B and C are three taps fixed to the bottom of a tank with d"}]},{"@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\/90844","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=90844"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90844\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90844"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90844"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90844"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}