{"id":92377,"date":"2025-06-01T11:22:29","date_gmt":"2025-06-01T11:22:29","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92377"},"modified":"2025-06-01T11:22:29","modified_gmt":"2025-06-01T11:22:29","slug":"a-and-b-can-complete-a-work-in-2-hours-and-55-minutes-a-alone-c","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-can-complete-a-work-in-2-hours-and-55-minutes-a-alone-c\/","title":{"rendered":"‘A’ and ‘B’ can complete a work in 2 hours and 55 minutes. ‘A’ alone c"},"content":{"rendered":"

‘A’ and ‘B’ can complete a work in 2 hours and 55 minutes. ‘A’ alone can do the same work two hours faster than ‘B’ alone can. How long will ‘B’ take to do the work alone ?<\/p>\n

[amp_mcq option1=”2 hours and 10 minutes” option2=”4 hours and 10 minutes” option3=”5 hours” option4=”7 hours” correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2017<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is D.
\n<\/section>\n
\nLet the time taken by B to complete the work alone be `x` hours.
\nSince A can do the same work two hours faster than B, the time taken by A alone is `x – 2` hours.
\nThe work rate of B is 1\/x work per hour.
\nThe work rate of A is 1\/(x-2) work per hour.
\nA and B together complete the work in 2 hours and 55 minutes.
\n2 hours 55 minutes = 2 + 55\/60 hours = 2 + 11\/12 hours = (24+11)\/12 hours = 35\/12 hours.
\nThe combined work rate of A and B is 1 \/ (35\/12) = 12\/35 work per hour.
\nThe combined work rate is also the sum of their individual rates: 1\/(x-2) + 1\/x = 12\/35.
\n<\/section>\n
\nTo solve for x:
\n[x + (x-2)] \/ [x(x-2)] = 12\/35
\n(2x – 2) \/ (x\u00b2 – 2x) = 12\/35
\n35(2x – 2) = 12(x\u00b2 – 2x)
\n70x – 70 = 12x\u00b2 – 24x
\n12x\u00b2 – 94x + 70 = 0
\nDivide by 2: 6x\u00b2 – 47x + 35 = 0
\nUsing the quadratic formula x = [-b \u00b1 sqrt(b\u00b2 – 4ac)] \/ 2a:
\nx = [47 \u00b1 sqrt((-47)\u00b2 – 4 * 6 * 35)] \/ (2 * 6)
\nx = [47 \u00b1 sqrt(2209 – 840)] \/ 12
\nx = [47 \u00b1 sqrt(1369)] \/ 12
\nx = [47 \u00b1 37] \/ 12
\nTwo possible solutions for x:
\nx1 = (47 + 37) \/ 12 = 84 \/ 12 = 7
\nx2 = (47 – 37) \/ 12 = 10 \/ 12 = 5\/6
\nIf x = 5\/6 hours, then A takes x – 2 = 5\/6 – 2 = -7\/6 hours, which is not possible as time cannot be negative.
\nSo, x = 7 hours is the valid solution.
\nB takes 7 hours to do the work alone.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

‘A’ and ‘B’ can complete a work in 2 hours and 55 minutes. ‘A’ alone can do the same work two hours faster than ‘B’ alone can. How long will ‘B’ take to do the work alone ? [amp_mcq option1=”2 hours and 10 minutes” option2=”4 hours and 10 minutes” option3=”5 hours” option4=”7 hours” correct=”option4″] This … <\/p>\n

Detailed Solution‘A’ and ‘B’ can complete a work in 2 hours and 55 minutes. ‘A’ alone c<\/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":[1101,1102],"class_list":["post-92377","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1101","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\n'A' and 'B' can complete a work in 2 hours and 55 minutes. 'A' alone c<\/title>\n<meta name=\"description\" content=\"The correct answer is D. Let the time taken by B to complete the work alone be `x` hours. Since A can do the same work two hours faster than B, the time taken by A alone is `x - 2` hours. The work rate of B is 1\/x work per hour. The work rate of A is 1\/(x-2) work per hour. A and B together complete the work in 2 hours and 55 minutes. 2 hours 55 minutes = 2 + 55\/60 hours = 2 + 11\/12 hours = (24+11)\/12 hours = 35\/12 hours. The combined work rate of A and B is 1 \/ (35\/12) = 12\/35 work per hour. The combined work rate is also the sum of their individual rates: 1\/(x-2) + 1\/x = 12\/35.\" \/>\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-and-b-can-complete-a-work-in-2-hours-and-55-minutes-a-alone-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"'A' and 'B' can complete a work in 2 hours and 55 minutes. 'A' alone c\" \/>\n<meta property=\"og:description\" content=\"The correct answer is D. Let the time taken by B to complete the work alone be `x` hours. Since A can do the same work two hours faster than B, the time taken by A alone is `x - 2` hours. The work rate of B is 1\/x work per hour. The work rate of A is 1\/(x-2) work per hour. A and B together complete the work in 2 hours and 55 minutes. 2 hours 55 minutes = 2 + 55\/60 hours = 2 + 11\/12 hours = (24+11)\/12 hours = 35\/12 hours. The combined work rate of A and B is 1 \/ (35\/12) = 12\/35 work per hour. The combined work rate is also the sum of their individual rates: 1\/(x-2) + 1\/x = 12\/35.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-and-b-can-complete-a-work-in-2-hours-and-55-minutes-a-alone-c\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:22:29+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' and 'B' can complete a work in 2 hours and 55 minutes. 'A' alone c","description":"The correct answer is D. Let the time taken by B to complete the work alone be `x` hours. Since A can do the same work two hours faster than B, the time taken by A alone is `x - 2` hours. The work rate of B is 1\/x work per hour. The work rate of A is 1\/(x-2) work per hour. A and B together complete the work in 2 hours and 55 minutes. 2 hours 55 minutes = 2 + 55\/60 hours = 2 + 11\/12 hours = (24+11)\/12 hours = 35\/12 hours. The combined work rate of A and B is 1 \/ (35\/12) = 12\/35 work per hour. The combined work rate is also the sum of their individual rates: 1\/(x-2) + 1\/x = 12\/35.","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-and-b-can-complete-a-work-in-2-hours-and-55-minutes-a-alone-c\/","og_locale":"en_US","og_type":"article","og_title":"'A' and 'B' can complete a work in 2 hours and 55 minutes. 'A' alone c","og_description":"The correct answer is D. Let the time taken by B to complete the work alone be `x` hours. Since A can do the same work two hours faster than B, the time taken by A alone is `x - 2` hours. The work rate of B is 1\/x work per hour. The work rate of A is 1\/(x-2) work per hour. A and B together complete the work in 2 hours and 55 minutes. 2 hours 55 minutes = 2 + 55\/60 hours = 2 + 11\/12 hours = (24+11)\/12 hours = 35\/12 hours. The combined work rate of A and B is 1 \/ (35\/12) = 12\/35 work per hour. 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