{"id":89979,"date":"2025-06-01T10:18:28","date_gmt":"2025-06-01T10:18:28","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=89979"},"modified":"2025-06-01T10:18:28","modified_gmt":"2025-06-01T10:18:28","slug":"a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/","title":{"rendered":"A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic"},"content":{"rendered":"

A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehicle gets some defect as a result of which 0.5 L of fuel gets wasted per hour when the engine is on. With what minimum speed the vehicle has to move to travel 20 km with the existing amount of fuel, if it travels with a uniform speed ?<\/p>\n

[amp_mcq option1=”100 km per hour” option2=”120 km per hour” option3=”150 km per hour” option4=”200 km per hour” correct=”option1″]<\/p>\n

\n
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This question was previously asked in<\/div>\n
UPSC CAPF – 2016<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour.<\/section>\n
Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km.
\nThe time taken for the journey is T = Distance \/ Speed = 20\/S hours.
\nThe fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L.
\nThe defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on.
\nTotal fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L.
\nTotal fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S.
\nThe available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel:
\n4\/3 + 10\/S <= 2\n10\/S <= 2 - 4\/3\n10\/S <= (6 - 4)\/3\n10\/S <= 2\/3\nTo find the minimum speed S, we rearrange the inequality:\nS\/10 >= 3\/2
\nS >= 10 * (3\/2)
\nS >= 15 km\/hour.
\nThe minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.<\/section>\n
The problem illustrates how time-dependent fuel consumption (wastage) interacts with speed and distance. Higher speed reduces travel time, thereby reducing total fuel wastage, even if the rate of wastage per hour is constant.<\/section>\n","protected":false},"excerpt":{"rendered":"

A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehicle gets some defect as a result of which 0.5 L of fuel gets wasted per hour when the engine is on. With what minimum speed the vehicle has to move to travel 20 km with the existing amount of fuel, … <\/p>\n

Detailed SolutionA vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic<\/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":[1098,1102],"class_list":["post-89979","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1098","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic<\/title>\n<meta name=\"description\" content=\"The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour. Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km. The time taken for the journey is T = Distance \/ Speed = 20\/S hours. The fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L. The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on. Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L. Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S. The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel: 4\/3 + 10\/S <= 2 10\/S <= 2 - 4\/3 10\/S <= (6 - 4)\/3 10\/S = 3\/2 S >= 10 * (3\/2) S >= 15 km\/hour. The minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.\" \/>\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-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic\" \/>\n<meta property=\"og:description\" content=\"The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour. Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km. The time taken for the journey is T = Distance \/ Speed = 20\/S hours. The fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L. The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on. Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L. Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S. The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel: 4\/3 + 10\/S <= 2 10\/S <= 2 - 4\/3 10\/S <= (6 - 4)\/3 10\/S = 3\/2 S >= 10 * (3\/2) S >= 15 km\/hour. The minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:18:28+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic","description":"The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour. Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km. The time taken for the journey is T = Distance \/ Speed = 20\/S hours. The fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L. The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on. Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L. Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S. The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel: 4\/3 + 10\/S <= 2 10\/S <= 2 - 4\/3 10\/S <= (6 - 4)\/3 10\/S = 3\/2 S >= 10 * (3\/2) S >= 15 km\/hour. The minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.","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-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/","og_locale":"en_US","og_type":"article","og_title":"A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic","og_description":"The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour. Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km. The time taken for the journey is T = Distance \/ Speed = 20\/S hours. The fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L. The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on. Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L. Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S. The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel: 4\/3 + 10\/S <= 2 10\/S <= 2 - 4\/3 10\/S <= (6 - 4)\/3 10\/S = 3\/2 S >= 10 * (3\/2) S >= 15 km\/hour. The minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:18:28+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/","name":"A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:18:28+00:00","dateModified":"2025-06-01T10:18:28+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The minimum speed required to complete the 20 km journey with 2 L of fuel is 15 km per hour. Among the given options, the minimum speed that is sufficient is 100 km per hour. Let S be the speed of the vehicle in km\/h. The distance to travel is 20 km. The time taken for the journey is T = Distance \/ Speed = 20\/S hours. The fuel consumed for the travel based on mileage is (Distance \/ Mileage) = 20 km \/ (15 km\/L) = 20\/15 L = 4\/3 L. The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on. Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20\/S) = 10\/S L. Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4\/3 + 10\/S. The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel: 4\/3 + 10\/S <= 2 10\/S <= 2 - 4\/3 10\/S <= (6 - 4)\/3 10\/S = 3\/2 S >= 10 * (3\/2) S >= 15 km\/hour. The minimum speed required is 15 km\/hour. All options (100, 120, 150, 200 km\/hour) are greater than 15 km\/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-vehicle-with-mileage-15-km-per-litre-contains-2-l-of-fuel-the-vehic\/#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 vehicle with mileage 15 km per litre contains 2 L of fuel. The vehic"}]},{"@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\/89979","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=89979"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/89979\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=89979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=89979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=89979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}