{"id":92516,"date":"2025-06-01T11:27:10","date_gmt":"2025-06-01T11:27:10","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92516"},"modified":"2025-06-01T11:27:10","modified_gmt":"2025-06-01T11:27:10","slug":"a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/","title":{"rendered":"A dog wants to catch a cat that is twenty-seven steps ahead of him. Th"},"content":{"rendered":"

A dog wants to catch a cat that is twenty-seven steps ahead of him. The cat takes eight steps to every five steps taken by the dog. Two steps of the dog are equal to five steps of the cat. How many steps of the dog will be required to catch the cat ?<\/p>\n

[amp_mcq option1=”28″ option2=”30″ option3=”48″ option4=”75″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe dog will require 30 steps to catch the cat.
\n<\/section>\n
\nLet D_d be the distance covered by one dog step and D_c be the distance covered by one cat step.
\nWe are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c.
\nThe cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c.<\/p>\n

In a certain time interval, the cat takes 8 steps and the dog takes 5 steps.
\nDistance covered by cat in this interval = 8 * D_c.
\nDistance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c.<\/p>\n

In this time interval, the dog reduces the distance between them by (Distance covered by dog) – (Distance covered by cat) = 12.5 * D_c – 8 * D_c = 4.5 * D_c.<\/p>\n

The total distance the dog needs to close is the initial distance, which is 27 * D_c.
\nNumber of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval)
\nNumber of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals.<\/p>\n

In each interval, the dog takes 5 steps.
\nTotal dog steps required = Number of intervals * Steps taken by dog per interval
\nTotal dog steps = 6 * 5 = 30 steps.
\n<\/section>\n

\nLet’s check the result:
\nAfter 30 dog steps, the dog covers 30 * D_d = 30 * (5\/2) * D_c = 75 * D_c.
\nThe dog takes 5 steps per interval, so 30 dog steps means 30\/5 = 6 intervals have passed.
\nIn 6 intervals, the cat takes 6 * 8 = 48 steps.
\nThe cat started 27 * D_c ahead. Its final position is 27 * D_c + 48 * D_c = 75 * D_c.
\nThe dog’s final position is 75 * D_c. The dog catches the cat when their positions are the same.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A dog wants to catch a cat that is twenty-seven steps ahead of him. The cat takes eight steps to every five steps taken by the dog. Two steps of the dog are equal to five steps of the cat. How many steps of the dog will be required to catch the cat ? [amp_mcq … <\/p>\n

Detailed SolutionA dog wants to catch a cat that is twenty-seven steps ahead of him. Th<\/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":[1114,1102],"class_list":["post-92516","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA dog wants to catch a cat that is twenty-seven steps ahead of him. Th<\/title>\n<meta name=\"description\" content=\"The dog will require 30 steps to catch the cat. Let D_d be the distance covered by one dog step and D_c be the distance covered by one cat step. We are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c. The cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c. In a certain time interval, the cat takes 8 steps and the dog takes 5 steps. Distance covered by cat in this interval = 8 * D_c. Distance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c. In this time interval, the dog reduces the distance between them by (Distance covered by dog) - (Distance covered by cat) = 12.5 * D_c - 8 * D_c = 4.5 * D_c. The total distance the dog needs to close is the initial distance, which is 27 * D_c. Number of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval) Number of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals. In each interval, the dog takes 5 steps. Total dog steps required = Number of intervals * Steps taken by dog per interval Total dog steps = 6 * 5 = 30 steps.\" \/>\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-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A dog wants to catch a cat that is twenty-seven steps ahead of him. Th\" \/>\n<meta property=\"og:description\" content=\"The dog will require 30 steps to catch the cat. Let D_d be the distance covered by one dog step and D_c be the distance covered by one cat step. We are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c. The cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c. In a certain time interval, the cat takes 8 steps and the dog takes 5 steps. Distance covered by cat in this interval = 8 * D_c. Distance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c. In this time interval, the dog reduces the distance between them by (Distance covered by dog) - (Distance covered by cat) = 12.5 * D_c - 8 * D_c = 4.5 * D_c. The total distance the dog needs to close is the initial distance, which is 27 * D_c. Number of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval) Number of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals. In each interval, the dog takes 5 steps. Total dog steps required = Number of intervals * Steps taken by dog per interval Total dog steps = 6 * 5 = 30 steps.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:27:10+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 dog wants to catch a cat that is twenty-seven steps ahead of him. Th","description":"The dog will require 30 steps to catch the cat. Let D_d be the distance covered by one dog step and D_c be the distance covered by one cat step. We are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c. The cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c. In a certain time interval, the cat takes 8 steps and the dog takes 5 steps. Distance covered by cat in this interval = 8 * D_c. Distance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c. In this time interval, the dog reduces the distance between them by (Distance covered by dog) - (Distance covered by cat) = 12.5 * D_c - 8 * D_c = 4.5 * D_c. The total distance the dog needs to close is the initial distance, which is 27 * D_c. Number of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval) Number of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals. In each interval, the dog takes 5 steps. Total dog steps required = Number of intervals * Steps taken by dog per interval Total dog steps = 6 * 5 = 30 steps.","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-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/","og_locale":"en_US","og_type":"article","og_title":"A dog wants to catch a cat that is twenty-seven steps ahead of him. Th","og_description":"The dog will require 30 steps to catch the cat. Let D_d be the distance covered by one dog step and D_c be the distance covered by one cat step. We are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c. The cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c. In a certain time interval, the cat takes 8 steps and the dog takes 5 steps. Distance covered by cat in this interval = 8 * D_c. Distance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c. In this time interval, the dog reduces the distance between them by (Distance covered by dog) - (Distance covered by cat) = 12.5 * D_c - 8 * D_c = 4.5 * D_c. The total distance the dog needs to close is the initial distance, which is 27 * D_c. Number of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval) Number of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals. In each interval, the dog takes 5 steps. Total dog steps required = Number of intervals * Steps taken by dog per interval Total dog steps = 6 * 5 = 30 steps.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:27:10+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-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/","name":"A dog wants to catch a cat that is twenty-seven steps ahead of him. Th","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:27:10+00:00","dateModified":"2025-06-01T11:27:10+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The dog will require 30 steps to catch the cat. Let D_d be the distance covered by one dog step and D_c be the distance covered by one cat step. We are given that 2 dog steps are equal to 5 cat steps in distance: 2 * D_d = 5 * D_c => D_d = (5\/2) * D_c. The cat starts 27 steps ahead of the dog. The initial distance between them is 27 * D_c. In a certain time interval, the cat takes 8 steps and the dog takes 5 steps. Distance covered by cat in this interval = 8 * D_c. Distance covered by dog in this interval = 5 * D_d = 5 * (5\/2) * D_c = 25\/2 * D_c = 12.5 * D_c. In this time interval, the dog reduces the distance between them by (Distance covered by dog) - (Distance covered by cat) = 12.5 * D_c - 8 * D_c = 4.5 * D_c. The total distance the dog needs to close is the initial distance, which is 27 * D_c. Number of intervals required to catch the cat = (Total distance to cover) \/ (Distance reduced per interval) Number of intervals = (27 * D_c) \/ (4.5 * D_c) = 27 \/ 4.5 = 27 \/ (9\/2) = 27 * (2\/9) = 3 * 2 = 6 intervals. In each interval, the dog takes 5 steps. Total dog steps required = Number of intervals * Steps taken by dog per interval Total dog steps = 6 * 5 = 30 steps.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-dog-wants-to-catch-a-cat-that-is-twenty-seven-steps-ahead-of-him-th\/#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 dog wants to catch a cat that is twenty-seven steps ahead of him. 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