{"id":92283,"date":"2025-06-01T11:19:56","date_gmt":"2025-06-01T11:19:56","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92283"},"modified":"2025-06-01T11:19:56","modified_gmt":"2025-06-01T11:19:56","slug":"kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/","title":{"rendered":"Kumar completes a work in 8 days and Raj completes the same work in 16"},"content":{"rendered":"

Kumar completes a work in 8 days and Raj completes the same work in 16 days. In how many days can Kumar and Raj together complete the work?<\/p>\n

[amp_mcq option1=”$3\\frac{1}{3}$ days” option2=”$5\\frac{1}{3}$ days” option3=”$1\\frac{1}{3}$ days” option4=”$\\frac{1}{3}$ day” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CBI DSP LDCE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nKumar completes the work in 8 days, so his work rate is $\\frac{1}{8}$ of the work per day.
\nRaj completes the work in 16 days, so his work rate is $\\frac{1}{16}$ of the work per day.
\nWhen working together, their work rates add up.
\nCombined work rate = Work rate of Kumar + Work rate of Raj
\nCombined work rate = $\\frac{1}{8} + \\frac{1}{16}$ per day.
\nTo add the fractions, find a common denominator, which is 16.
\nCombined work rate = $\\frac{2}{16} + \\frac{1}{16} = \\frac{3}{16}$ of the work per day.
\nThe time taken to complete the work together is the reciprocal of the combined work rate.
\nTime taken together = $\\frac{1}{\\text{Combined work rate}} = \\frac{1}{\\frac{3}{16}} = \\frac{16}{3}$ days.
\nConverting the improper fraction to a mixed number: $\\frac{16}{3} = 5$ with a remainder of 1, so $5\\frac{1}{3}$ days.
\n<\/section>\n
\nIf a person completes a work in $n$ days, their work rate is $\\frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.
\n<\/section>\n
\nThis type of problem is a classic “work and time” problem. The formula for two people is $\\frac{1}{T} = \\frac{1}{T_1} + \\frac{1}{T_2}$, where $T_1$ and $T_2$ are the times taken by individuals and $T$ is the time taken together.
\n$\\frac{1}{T} = \\frac{1}{8} + \\frac{1}{16} = \\frac{2+1}{16} = \\frac{3}{16}$.
\n$T = \\frac{16}{3} = 5\\frac{1}{3}$ days.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Kumar completes a work in 8 days and Raj completes the same work in 16 days. In how many days can Kumar and Raj together complete the work? [amp_mcq option1=”$3\\frac{1}{3}$ days” option2=”$5\\frac{1}{3}$ days” option3=”$1\\frac{1}{3}$ days” option4=”$\\frac{1}{3}$ day” correct=”option2″] This question was previously asked in UPSC CBI DSP LDCE – 2023 Download PDFAttempt Online Kumar completes … <\/p>\n

Detailed SolutionKumar completes a work in 8 days and Raj completes the same work in 16<\/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":[1086],"tags":[1105,1102],"class_list":["post-92283","post","type-post","status-publish","format-standard","hentry","category-upsc-cbi-dsp-ldce","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nKumar completes a work in 8 days and Raj completes the same work in 16<\/title>\n<meta name=\"description\" content=\"Kumar completes the work in 8 days, so his work rate is $frac{1}{8}$ of the work per day. Raj completes the work in 16 days, so his work rate is $frac{1}{16}$ of the work per day. When working together, their work rates add up. Combined work rate = Work rate of Kumar + Work rate of Raj Combined work rate = $frac{1}{8} + frac{1}{16}$ per day. To add the fractions, find a common denominator, which is 16. Combined work rate = $frac{2}{16} + frac{1}{16} = frac{3}{16}$ of the work per day. The time taken to complete the work together is the reciprocal of the combined work rate. Time taken together = $frac{1}{text{Combined work rate}} = frac{1}{frac{3}{16}} = frac{16}{3}$ days. Converting the improper fraction to a mixed number: $frac{16}{3} = 5$ with a remainder of 1, so $5frac{1}{3}$ days. If a person completes a work in $n$ days, their work rate is $frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.\" \/>\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\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kumar completes a work in 8 days and Raj completes the same work in 16\" \/>\n<meta property=\"og:description\" content=\"Kumar completes the work in 8 days, so his work rate is $frac{1}{8}$ of the work per day. Raj completes the work in 16 days, so his work rate is $frac{1}{16}$ of the work per day. When working together, their work rates add up. Combined work rate = Work rate of Kumar + Work rate of Raj Combined work rate = $frac{1}{8} + frac{1}{16}$ per day. To add the fractions, find a common denominator, which is 16. Combined work rate = $frac{2}{16} + frac{1}{16} = frac{3}{16}$ of the work per day. The time taken to complete the work together is the reciprocal of the combined work rate. Time taken together = $frac{1}{text{Combined work rate}} = frac{1}{frac{3}{16}} = frac{16}{3}$ days. Converting the improper fraction to a mixed number: $frac{16}{3} = 5$ with a remainder of 1, so $5frac{1}{3}$ days. If a person completes a work in $n$ days, their work rate is $frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:19:56+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":"Kumar completes a work in 8 days and Raj completes the same work in 16","description":"Kumar completes the work in 8 days, so his work rate is $frac{1}{8}$ of the work per day. Raj completes the work in 16 days, so his work rate is $frac{1}{16}$ of the work per day. When working together, their work rates add up. Combined work rate = Work rate of Kumar + Work rate of Raj Combined work rate = $frac{1}{8} + frac{1}{16}$ per day. To add the fractions, find a common denominator, which is 16. Combined work rate = $frac{2}{16} + frac{1}{16} = frac{3}{16}$ of the work per day. The time taken to complete the work together is the reciprocal of the combined work rate. Time taken together = $frac{1}{text{Combined work rate}} = frac{1}{frac{3}{16}} = frac{16}{3}$ days. Converting the improper fraction to a mixed number: $frac{16}{3} = 5$ with a remainder of 1, so $5frac{1}{3}$ days. If a person completes a work in $n$ days, their work rate is $frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.","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\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/","og_locale":"en_US","og_type":"article","og_title":"Kumar completes a work in 8 days and Raj completes the same work in 16","og_description":"Kumar completes the work in 8 days, so his work rate is $frac{1}{8}$ of the work per day. Raj completes the work in 16 days, so his work rate is $frac{1}{16}$ of the work per day. When working together, their work rates add up. Combined work rate = Work rate of Kumar + Work rate of Raj Combined work rate = $frac{1}{8} + frac{1}{16}$ per day. To add the fractions, find a common denominator, which is 16. Combined work rate = $frac{2}{16} + frac{1}{16} = frac{3}{16}$ of the work per day. The time taken to complete the work together is the reciprocal of the combined work rate. Time taken together = $frac{1}{text{Combined work rate}} = frac{1}{frac{3}{16}} = frac{16}{3}$ days. Converting the improper fraction to a mixed number: $frac{16}{3} = 5$ with a remainder of 1, so $5frac{1}{3}$ days. If a person completes a work in $n$ days, their work rate is $frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:19:56+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\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/","url":"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/","name":"Kumar completes a work in 8 days and Raj completes the same work in 16","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:19:56+00:00","dateModified":"2025-06-01T11:19:56+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Kumar completes the work in 8 days, so his work rate is $\\frac{1}{8}$ of the work per day. Raj completes the work in 16 days, so his work rate is $\\frac{1}{16}$ of the work per day. When working together, their work rates add up. Combined work rate = Work rate of Kumar + Work rate of Raj Combined work rate = $\\frac{1}{8} + \\frac{1}{16}$ per day. To add the fractions, find a common denominator, which is 16. Combined work rate = $\\frac{2}{16} + \\frac{1}{16} = \\frac{3}{16}$ of the work per day. The time taken to complete the work together is the reciprocal of the combined work rate. Time taken together = $\\frac{1}{\\text{Combined work rate}} = \\frac{1}{\\frac{3}{16}} = \\frac{16}{3}$ days. Converting the improper fraction to a mixed number: $\\frac{16}{3} = 5$ with a remainder of 1, so $5\\frac{1}{3}$ days. If a person completes a work in $n$ days, their work rate is $\\frac{1}{n}$ of the work per day. When multiple people work together, their individual work rates add up to find the combined work rate. The total time taken is the reciprocal of the combined work rate.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/kumar-completes-a-work-in-8-days-and-raj-completes-the-same-work-in-16\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CBI DSP LDCE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cbi-dsp-ldce\/"},{"@type":"ListItem","position":3,"name":"Kumar completes a work in 8 days and Raj completes the same work in 16"}]},{"@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\/92283","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=92283"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92283\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92283"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92283"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}