{"id":92638,"date":"2025-06-01T11:29:38","date_gmt":"2025-06-01T11:29:38","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92638"},"modified":"2025-06-01T11:29:38","modified_gmt":"2025-06-01T11:29:38","slug":"a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/","title":{"rendered":"A water tank can be filled by a pipe in 4 minutes and by a smaller pip"},"content":{"rendered":"<p>A water tank can be filled by a pipe in 4 minutes and by a smaller pipe in 12 minutes. If both the pipes are opened simultaneously, in how much time will the tank be filled?<\/p>\n<p>[amp_mcq option1=&#8221;6 minutes&#8221; option2=&#8221;4 minutes&#8221; option3=&#8221;3 minutes&#8221; option4=&#8221;2 minutes&#8221; correct=&#8221;option3&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CISF-AC-EXE &#8211; 2019<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-cisf-ac-exe-2019.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-cisf-ac-exe-2019\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">\nLet the capacity of the water tank be V units.<br \/>\nThe first pipe can fill the tank in 4 minutes.<br \/>\nRate of filling by the first pipe = V \/ 4 units per minute.<br \/>\nWe can normalize the tank capacity to 1 unit (i.e., the whole tank).<br \/>\nRate of the first pipe = 1\/4 tank per minute.<\/p>\n<p>The smaller pipe can fill the tank in 12 minutes.<br \/>\nRate of filling by the second pipe = V \/ 12 units per minute.<br \/>\nNormalized rate of the second pipe = 1\/12 tank per minute.<\/p>\n<p>When both pipes are opened simultaneously, their rates of filling are added together.<br \/>\nCombined rate of both pipes = Rate of pipe 1 + Rate of pipe 2<br \/>\nCombined rate = 1\/4 + 1\/12 tanks per minute.<br \/>\nTo add the fractions, find a common denominator, which is 12.<br \/>\n1\/4 = 3\/12.<br \/>\nCombined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute.<br \/>\nCombined rate = 1\/3 tank per minute.<\/p>\n<p>The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank).<br \/>\nTime taken = 1 \/ (Combined rate)<br \/>\nTime taken = 1 \/ (1\/3) minutes.<br \/>\nTime taken = 3 minutes.<br \/>\n<\/section>\n<section id=\"pyq-key-points\">\n&#8211; When pipes work together to fill a tank, their filling rates are added.<br \/>\n&#8211; Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank).<br \/>\n&#8211; If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.<br \/>\n<\/section>\n<section id=\"pyq-additional-information\">\nThis type of problem is a standard work\/rate problem. The formula for two agents working together is $T_{combined} = \\frac{T_1 \\times T_2}{T_1 + T_2}$.<br \/>\nUsing this formula:<br \/>\n$T_{combined} = \\frac{4 \\times 12}{4 + 12} = \\frac{48}{16} = 3$ minutes.<br \/>\nThis formula is a shortcut derived from $1\/T_1 + 1\/T_2 = 1\/T_{combined}$.<br \/>\n$(T_2 + T_1) \/ (T_1 T_2) = 1\/T_{combined}$<br \/>\n$T_{combined} = (T_1 T_2) \/ (T_1 + T_2)$.<br \/>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>A water tank can be filled by a pipe in 4 minutes and by a smaller pipe in 12 minutes. If both the pipes are opened simultaneously, in how much time will the tank be filled? [amp_mcq option1=&#8221;6 minutes&#8221; option2=&#8221;4 minutes&#8221; option3=&#8221;3 minutes&#8221; option4=&#8221;2 minutes&#8221; correct=&#8221;option3&#8243;] This question was previously asked in UPSC CISF-AC-EXE &#8211; &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"A water tank can be filled by a pipe in 4 minutes and by a smaller pip\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/#more-92638\">Detailed Solution<span class=\"screen-reader-text\">A water tank can be filled by a pipe in 4 minutes and by a smaller pip<\/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":[1089],"tags":[1119,1102],"class_list":["post-92638","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1119","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A water tank can be filled by a pipe in 4 minutes and by a smaller pip<\/title>\n<meta name=\"description\" content=\"Let the capacity of the water tank be V units. The first pipe can fill the tank in 4 minutes. Rate of filling by the first pipe = V \/ 4 units per minute. We can normalize the tank capacity to 1 unit (i.e., the whole tank). Rate of the first pipe = 1\/4 tank per minute. The smaller pipe can fill the tank in 12 minutes. Rate of filling by the second pipe = V \/ 12 units per minute. Normalized rate of the second pipe = 1\/12 tank per minute. When both pipes are opened simultaneously, their rates of filling are added together. Combined rate of both pipes = Rate of pipe 1 + Rate of pipe 2 Combined rate = 1\/4 + 1\/12 tanks per minute. To add the fractions, find a common denominator, which is 12. 1\/4 = 3\/12. Combined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute. Combined rate = 1\/3 tank per minute. The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank). Time taken = 1 \/ (Combined rate) Time taken = 1 \/ (1\/3) minutes. Time taken = 3 minutes. - When pipes work together to fill a tank, their filling rates are added. - Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank). - If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.\" \/>\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-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A water tank can be filled by a pipe in 4 minutes and by a smaller pip\" \/>\n<meta property=\"og:description\" content=\"Let the capacity of the water tank be V units. The first pipe can fill the tank in 4 minutes. Rate of filling by the first pipe = V \/ 4 units per minute. We can normalize the tank capacity to 1 unit (i.e., the whole tank). Rate of the first pipe = 1\/4 tank per minute. The smaller pipe can fill the tank in 12 minutes. Rate of filling by the second pipe = V \/ 12 units per minute. Normalized rate of the second pipe = 1\/12 tank per minute. When both pipes are opened simultaneously, their rates of filling are added together. Combined rate of both pipes = Rate of pipe 1 + Rate of pipe 2 Combined rate = 1\/4 + 1\/12 tanks per minute. To add the fractions, find a common denominator, which is 12. 1\/4 = 3\/12. Combined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute. Combined rate = 1\/3 tank per minute. The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank). Time taken = 1 \/ (Combined rate) Time taken = 1 \/ (1\/3) minutes. Time taken = 3 minutes. - When pipes work together to fill a tank, their filling rates are added. - Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank). - If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:29:38+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 water tank can be filled by a pipe in 4 minutes and by a smaller pip","description":"Let the capacity of the water tank be V units. The first pipe can fill the tank in 4 minutes. Rate of filling by the first pipe = V \/ 4 units per minute. We can normalize the tank capacity to 1 unit (i.e., the whole tank). Rate of the first pipe = 1\/4 tank per minute. The smaller pipe can fill the tank in 12 minutes. Rate of filling by the second pipe = V \/ 12 units per minute. Normalized rate of the second pipe = 1\/12 tank per minute. When both pipes are opened simultaneously, their rates of filling are added together. Combined rate of both pipes = Rate of pipe 1 + Rate of pipe 2 Combined rate = 1\/4 + 1\/12 tanks per minute. To add the fractions, find a common denominator, which is 12. 1\/4 = 3\/12. Combined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute. Combined rate = 1\/3 tank per minute. The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank). Time taken = 1 \/ (Combined rate) Time taken = 1 \/ (1\/3) minutes. Time taken = 3 minutes. - When pipes work together to fill a tank, their filling rates are added. - Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank). - If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.","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-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/","og_locale":"en_US","og_type":"article","og_title":"A water tank can be filled by a pipe in 4 minutes and by a smaller pip","og_description":"Let the capacity of the water tank be V units. The first pipe can fill the tank in 4 minutes. Rate of filling by the first pipe = V \/ 4 units per minute. We can normalize the tank capacity to 1 unit (i.e., the whole tank). Rate of the first pipe = 1\/4 tank per minute. The smaller pipe can fill the tank in 12 minutes. Rate of filling by the second pipe = V \/ 12 units per minute. Normalized rate of the second pipe = 1\/12 tank per minute. When both pipes are opened simultaneously, their rates of filling are added together. Combined rate of both pipes = Rate of pipe 1 + Rate of pipe 2 Combined rate = 1\/4 + 1\/12 tanks per minute. To add the fractions, find a common denominator, which is 12. 1\/4 = 3\/12. Combined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute. Combined rate = 1\/3 tank per minute. The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank). Time taken = 1 \/ (Combined rate) Time taken = 1 \/ (1\/3) minutes. Time taken = 3 minutes. - When pipes work together to fill a tank, their filling rates are added. - Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank). - If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:29:38+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-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/","name":"A water tank can be filled by a pipe in 4 minutes and by a smaller pip","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:29:38+00:00","dateModified":"2025-06-01T11:29:38+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the capacity of the water tank be V units. The first pipe can fill the tank in 4 minutes. Rate of filling by the first pipe = V \/ 4 units per minute. We can normalize the tank capacity to 1 unit (i.e., the whole tank). Rate of the first pipe = 1\/4 tank per minute. The smaller pipe can fill the tank in 12 minutes. Rate of filling by the second pipe = V \/ 12 units per minute. Normalized rate of the second pipe = 1\/12 tank per minute. When both pipes are opened simultaneously, their rates of filling are added together. Combined rate of both pipes = Rate of pipe 1 + Rate of pipe 2 Combined rate = 1\/4 + 1\/12 tanks per minute. To add the fractions, find a common denominator, which is 12. 1\/4 = 3\/12. Combined rate = 3\/12 + 1\/12 = 4\/12 tanks per minute. Combined rate = 1\/3 tank per minute. The time taken to fill the tank is the reciprocal of the combined rate (since Rate * Time = Work Done, and Work Done = 1 tank). Time taken = 1 \/ (Combined rate) Time taken = 1 \/ (1\/3) minutes. Time taken = 3 minutes. - When pipes work together to fill a tank, their filling rates are added. - Rate = 1 \/ Time (where Time is the time taken to complete the whole work, i.e., fill the tank). - If pipes A and B take $T_A$ and $T_B$ time respectively to fill a tank, their combined rate is $1\/T_A + 1\/T_B$, and the time taken together is $1 \/ (1\/T_A + 1\/T_B)$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-water-tank-can-be-filled-by-a-pipe-in-4-minutes-and-by-a-smaller-pip\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"A water tank can be filled by a pipe in 4 minutes and by a smaller pip"}]},{"@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\/92638","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=92638"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92638\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}