{"id":92349,"date":"2025-06-01T11:21:54","date_gmt":"2025-06-01T11:21:54","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92349"},"modified":"2025-06-01T11:21:54","modified_gmt":"2025-06-01T11:21:54","slug":"x-paid-%e2%82%b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-%e2%82%b9-5-per-c","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/x-paid-%e2%82%b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-%e2%82%b9-5-per-c\/","title":{"rendered":"X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c"},"content":{"rendered":"

X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per cup and coffee costs \u20b9 8 per cup, which one of the following statements is correct ?<\/p>\n

[amp_mcq option1=”He drank 8 cups of tea and coffee.” option2=”He drank the same number of cups of tea and coffee.” option3=”He drank more tea than coffee.” option4=”He drank more coffee than tea.” 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
\nHe drank more coffee than tea.
\n<\/section>\n
\nLet ‘t’ be the number of cups of tea and ‘c’ be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c.
\nWe can try possible values for c:
\nIf c=0, 5t = 47 (not possible for integer t)
\nIf c=1, 5t = 47 – 8 = 39 (not possible for integer t)
\nIf c=2, 5t = 47 – 16 = 31 (not possible for integer t)
\nIf c=3, 5t = 47 – 24 = 23 (not possible for integer t)
\nIf c=4, 5t = 47 – 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4).
\nIf c=5, 5t = 47 – 40 = 7 (not possible for integer t)
\nIf c=6, 5t = 47 – 48 = -1 (not possible for non-negative t)
\nThe only valid solution is t=3 cups of tea and c=4 cups of coffee.
\nBased on this solution:
\nA) Total cups = 3 + 4 = 7, not 8. (Incorrect)
\nB) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect)
\nC) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect)
\nD) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)
\n<\/section>\n
\nThis is a simple linear Diophantine equation where we are looking for non-negative integer solutions. Since the coefficients are relatively small, trial and error is an efficient method to find the solution.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per cup and coffee costs \u20b9 8 per cup, which one of the following statements is correct ? [amp_mcq option1=”He drank 8 cups of tea and coffee.” option2=”He drank the same number of cups of tea and coffee.” option3=”He … <\/p>\n

Detailed SolutionX paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per 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-92349","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":"\nX paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c<\/title>\n<meta name=\"description\" content=\"He drank more coffee than tea. Let 't' be the number of cups of tea and 'c' be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c. We can try possible values for c: If c=0, 5t = 47 (not possible for integer t) If c=1, 5t = 47 - 8 = 39 (not possible for integer t) If c=2, 5t = 47 - 16 = 31 (not possible for integer t) If c=3, 5t = 47 - 24 = 23 (not possible for integer t) If c=4, 5t = 47 - 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4). If c=5, 5t = 47 - 40 = 7 (not possible for integer t) If c=6, 5t = 47 - 48 = -1 (not possible for non-negative t) The only valid solution is t=3 cups of tea and c=4 cups of coffee. Based on this solution: A) Total cups = 3 + 4 = 7, not 8. (Incorrect) B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect) C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect) D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)\" \/>\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\/x-paid-\u20b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-\u20b9-5-per-c\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c\" \/>\n<meta property=\"og:description\" content=\"He drank more coffee than tea. Let 't' be the number of cups of tea and 'c' be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c. We can try possible values for c: If c=0, 5t = 47 (not possible for integer t) If c=1, 5t = 47 - 8 = 39 (not possible for integer t) If c=2, 5t = 47 - 16 = 31 (not possible for integer t) If c=3, 5t = 47 - 24 = 23 (not possible for integer t) If c=4, 5t = 47 - 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4). If c=5, 5t = 47 - 40 = 7 (not possible for integer t) If c=6, 5t = 47 - 48 = -1 (not possible for non-negative t) The only valid solution is t=3 cups of tea and c=4 cups of coffee. Based on this solution: A) Total cups = 3 + 4 = 7, not 8. (Incorrect) B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect) C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect) D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/x-paid-\u20b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-\u20b9-5-per-c\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:21:54+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":"X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c","description":"He drank more coffee than tea. Let 't' be the number of cups of tea and 'c' be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c. We can try possible values for c: If c=0, 5t = 47 (not possible for integer t) If c=1, 5t = 47 - 8 = 39 (not possible for integer t) If c=2, 5t = 47 - 16 = 31 (not possible for integer t) If c=3, 5t = 47 - 24 = 23 (not possible for integer t) If c=4, 5t = 47 - 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4). If c=5, 5t = 47 - 40 = 7 (not possible for integer t) If c=6, 5t = 47 - 48 = -1 (not possible for non-negative t) The only valid solution is t=3 cups of tea and c=4 cups of coffee. Based on this solution: A) Total cups = 3 + 4 = 7, not 8. (Incorrect) B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect) C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect) D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)","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\/x-paid-\u20b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-\u20b9-5-per-c\/","og_locale":"en_US","og_type":"article","og_title":"X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c","og_description":"He drank more coffee than tea. Let 't' be the number of cups of tea and 'c' be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c. We can try possible values for c: If c=0, 5t = 47 (not possible for integer t) If c=1, 5t = 47 - 8 = 39 (not possible for integer t) If c=2, 5t = 47 - 16 = 31 (not possible for integer t) If c=3, 5t = 47 - 24 = 23 (not possible for integer t) If c=4, 5t = 47 - 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4). If c=5, 5t = 47 - 40 = 7 (not possible for integer t) If c=6, 5t = 47 - 48 = -1 (not possible for non-negative t) The only valid solution is t=3 cups of tea and c=4 cups of coffee. Based on this solution: A) Total cups = 3 + 4 = 7, not 8. (Incorrect) B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect) C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect) D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. (Correct)","og_url":"https:\/\/exam.pscnotes.com\/mcq\/x-paid-\u20b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-\u20b9-5-per-c\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:21:54+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\/x-paid-%e2%82%b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-%e2%82%b9-5-per-c\/","url":"https:\/\/exam.pscnotes.com\/mcq\/x-paid-%e2%82%b9-47-for-certain-cups-of-tea-and-coffee-if-tea-costs-%e2%82%b9-5-per-c\/","name":"X paid \u20b9 47 for certain cups of tea and coffee. If tea costs \u20b9 5 per c","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:21:54+00:00","dateModified":"2025-06-01T11:21:54+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"He drank more coffee than tea. Let 't' be the number of cups of tea and 'c' be the number of cups of coffee. The cost equation is 5t + 8c = 47. We need to find non-negative integer solutions for t and c. We can try possible values for c: If c=0, 5t = 47 (not possible for integer t) If c=1, 5t = 47 - 8 = 39 (not possible for integer t) If c=2, 5t = 47 - 16 = 31 (not possible for integer t) If c=3, 5t = 47 - 24 = 23 (not possible for integer t) If c=4, 5t = 47 - 32 = 15 => t = 3. This is a valid integer solution (t=3, c=4). If c=5, 5t = 47 - 40 = 7 (not possible for integer t) If c=6, 5t = 47 - 48 = -1 (not possible for non-negative t) The only valid solution is t=3 cups of tea and c=4 cups of coffee. Based on this solution: A) Total cups = 3 + 4 = 7, not 8. (Incorrect) B) Number of tea cups (3) is not the same as coffee cups (4). (Incorrect) C) He drank 3 cups of tea and 4 cups of coffee. 3 is not more than 4. (Incorrect) D) He drank 4 cups of coffee and 3 cups of tea. 4 is more than 3. 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