{"id":93422,"date":"2025-06-01T11:50:14","date_gmt":"2025-06-01T11:50:14","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93422"},"modified":"2025-06-01T11:50:14","modified_gmt":"2025-06-01T11:50:14","slug":"assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/","title":{"rendered":"Assume there to be some foodstuff that is sufficient for a team for $x"},"content":{"rendered":"

Assume there to be some foodstuff that is sufficient for a team for $x$ number of days. After 20 days, 25% of team members happen to quit. It is observed that the remaining foodstuff is sufficient to feed the remaining members for another $x$ number of days. What is the value of $x$?<\/p>\n

[amp_mcq option1=”80″ option2=”72″ option3=”60″ option4=”40″ correct=”option1″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is 80.
\n<\/section>\n
\nThis is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts.
\nLet the initial number of team members be M.
\nThe food is sufficient for M members for x days. Total food “units” can be represented as M * x.
\nAfter 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units.
\nThe remaining food units = (Initial food) – (Food consumed) = M * x – M * 20 = M(x – 20).
\nAfter 20 days, 25% of the team members quit.
\nThe remaining number of team members = M – 25% of M = M – 0.25M = 0.75M.
\nIt is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days.
\nSo, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x.
\nEquating the two expressions for the remaining food:
\nM(x – 20) = 0.75M * x
\nSince M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M:
\nx – 20 = 0.75x
\nNow, solve for x:
\nx – 0.75x = 20
\n0.25x = 20
\nx = 20 \/ 0.25
\nx = 20 \/ (1\/4)
\nx = 20 * 4
\nx = 80.
\n<\/section>\n
\nThis type of problem relies on the principle that the total amount of work (or food) is directly proportional to the number of workers (or members) and the time they work (or are fed). If N workers can do a job in D days, the total work is N*D units. Similarly, if N members have food for D days, the total food is N*D units. When the number of workers or the duration changes, the total work or remaining work can be related using this principle.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Assume there to be some foodstuff that is sufficient for a team for $x$ number of days. After 20 days, 25% of team members happen to quit. It is observed that the remaining foodstuff is sufficient to feed the remaining members for another $x$ number of days. What is the value of $x$? [amp_mcq option1=”80″ … <\/p>\n

Detailed SolutionAssume there to be some foodstuff that is sufficient for a team for $x<\/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":[1103,1102],"class_list":["post-93422","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nAssume there to be some foodstuff that is sufficient for a team for $x<\/title>\n<meta name=\"description\" content=\"The correct answer is 80. This is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts. Let the initial number of team members be M. The food is sufficient for M members for x days. Total food "units" can be represented as M * x. After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units. The remaining food units = (Initial food) - (Food consumed) = M * x - M * 20 = M(x - 20). After 20 days, 25% of the team members quit. The remaining number of team members = M - 25% of M = M - 0.25M = 0.75M. It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days. So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x. Equating the two expressions for the remaining food: M(x - 20) = 0.75M * x Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M: x - 20 = 0.75x Now, solve for x: x - 0.75x = 20 0.25x = 20 x = 20 \/ 0.25 x = 20 \/ (1\/4) x = 20 * 4 x = 80.\" \/>\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\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Assume there to be some foodstuff that is sufficient for a team for $x\" \/>\n<meta property=\"og:description\" content=\"The correct answer is 80. This is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts. Let the initial number of team members be M. The food is sufficient for M members for x days. Total food "units" can be represented as M * x. After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units. The remaining food units = (Initial food) - (Food consumed) = M * x - M * 20 = M(x - 20). After 20 days, 25% of the team members quit. The remaining number of team members = M - 25% of M = M - 0.25M = 0.75M. It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days. So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x. Equating the two expressions for the remaining food: M(x - 20) = 0.75M * x Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M: x - 20 = 0.75x Now, solve for x: x - 0.75x = 20 0.25x = 20 x = 20 \/ 0.25 x = 20 \/ (1\/4) x = 20 * 4 x = 80.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:50:14+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":"Assume there to be some foodstuff that is sufficient for a team for $x","description":"The correct answer is 80. This is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts. Let the initial number of team members be M. The food is sufficient for M members for x days. Total food \"units\" can be represented as M * x. After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units. The remaining food units = (Initial food) - (Food consumed) = M * x - M * 20 = M(x - 20). After 20 days, 25% of the team members quit. The remaining number of team members = M - 25% of M = M - 0.25M = 0.75M. It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days. So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x. Equating the two expressions for the remaining food: M(x - 20) = 0.75M * x Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M: x - 20 = 0.75x Now, solve for x: x - 0.75x = 20 0.25x = 20 x = 20 \/ 0.25 x = 20 \/ (1\/4) x = 20 * 4 x = 80.","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\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/","og_locale":"en_US","og_type":"article","og_title":"Assume there to be some foodstuff that is sufficient for a team for $x","og_description":"The correct answer is 80. This is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts. Let the initial number of team members be M. The food is sufficient for M members for x days. Total food \"units\" can be represented as M * x. After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units. The remaining food units = (Initial food) - (Food consumed) = M * x - M * 20 = M(x - 20). After 20 days, 25% of the team members quit. The remaining number of team members = M - 25% of M = M - 0.25M = 0.75M. It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days. So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x. Equating the two expressions for the remaining food: M(x - 20) = 0.75M * x Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M: x - 20 = 0.75x Now, solve for x: x - 0.75x = 20 0.25x = 20 x = 20 \/ 0.25 x = 20 \/ (1\/4) x = 20 * 4 x = 80.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:50:14+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\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/","url":"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/","name":"Assume there to be some foodstuff that is sufficient for a team for $x","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:50:14+00:00","dateModified":"2025-06-01T11:50:14+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is 80. This is a variation of a work\/provision problem. The total amount of food is proportional to the number of team members multiplied by the number of days it lasts. Let the initial number of team members be M. The food is sufficient for M members for x days. Total food \"units\" can be represented as M * x. After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units. The remaining food units = (Initial food) - (Food consumed) = M * x - M * 20 = M(x - 20). After 20 days, 25% of the team members quit. The remaining number of team members = M - 25% of M = M - 0.25M = 0.75M. It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days. So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x. Equating the two expressions for the remaining food: M(x - 20) = 0.75M * x Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M: x - 20 = 0.75x Now, solve for x: x - 0.75x = 20 0.25x = 20 x = 20 \/ 0.25 x = 20 \/ (1\/4) x = 20 * 4 x = 80.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/assume-there-to-be-some-foodstuff-that-is-sufficient-for-a-team-for-x\/#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":"Assume there to be some foodstuff that is sufficient for a team for $x"}]},{"@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\/93422","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=93422"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93422\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}