{"id":90726,"date":"2025-06-01T10:35:26","date_gmt":"2025-06-01T10:35:26","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90726"},"modified":"2025-06-01T10:35:26","modified_gmt":"2025-06-01T10:35:26","slug":"a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/","title":{"rendered":"A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If"},"content":{"rendered":"

A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If the total value of the coins is \u20b9 320, then the number of \u20b9 2 coins is<\/p>\n

[amp_mcq option1=”40″ option2=”50″ option3=”60″ option4=”70″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins.
\nWe are given two pieces of information:
\n1. The total number of coins is 100: x + y = 100
\n2. The total value of the coins is \u20b9 320: 2x + 5y = 320
\nWe have a system of two linear equations with two variables. We want to find the value of x.
\nFrom the first equation, we can express y as y = 100 – x.
\nSubstitute this into the second equation:
\n2x + 5(100 – x) = 320
\n2x + 500 – 5x = 320
\n500 – 3x = 320
\n500 – 320 = 3x
\n180 = 3x
\nx = 180 \/ 3 = 60.
\nSo, there are 60 coins of \u20b9 2.
\nIf x = 60, then y = 100 – 60 = 40.
\nCheck the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct.
\n<\/section>\n
\n– Set up a system of linear equations based on the problem statement.
\n– One equation represents the total count of items.
\n– Another equation represents the total value based on the count and individual item values.
\n– Solve the system of equations using substitution or elimination to find the required variable.
\n<\/section>\n
\nThis is a standard word problem that translates into a system of linear equations, often encountered in basic algebra and quantitative aptitude tests. The variables represent the counts of different denominations, and the equations represent the total count and the total value.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If the total value of the coins is \u20b9 320, then the number of \u20b9 2 coins is [amp_mcq option1=”40″ option2=”50″ option3=”60″ option4=”70″ correct=”option3″] This question was previously asked in UPSC CAPF – 2022 Download PDFAttempt Online Let x … <\/p>\n

Detailed SolutionA person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If<\/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":[1108,1102],"class_list":["post-90726","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If<\/title>\n<meta name=\"description\" content=\"Let x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins. We are given two pieces of information: 1. The total number of coins is 100: x + y = 100 2. The total value of the coins is \u20b9 320: 2x + 5y = 320 We have a system of two linear equations with two variables. We want to find the value of x. From the first equation, we can express y as y = 100 - x. Substitute this into the second equation: 2x + 5(100 - x) = 320 2x + 500 - 5x = 320 500 - 3x = 320 500 - 320 = 3x 180 = 3x x = 180 \/ 3 = 60. So, there are 60 coins of \u20b9 2. If x = 60, then y = 100 - 60 = 40. Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct. - Set up a system of linear equations based on the problem statement. - One equation represents the total count of items. - Another equation represents the total value based on the count and individual item values. - Solve the system of equations using substitution or elimination to find the required variable.\" \/>\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-person-has-a-total-of-100-coins-consisting-of-\u20b9-2-and-\u20b9-5-coins-if\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If\" \/>\n<meta property=\"og:description\" content=\"Let x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins. We are given two pieces of information: 1. The total number of coins is 100: x + y = 100 2. The total value of the coins is \u20b9 320: 2x + 5y = 320 We have a system of two linear equations with two variables. We want to find the value of x. From the first equation, we can express y as y = 100 - x. Substitute this into the second equation: 2x + 5(100 - x) = 320 2x + 500 - 5x = 320 500 - 3x = 320 500 - 320 = 3x 180 = 3x x = 180 \/ 3 = 60. So, there are 60 coins of \u20b9 2. If x = 60, then y = 100 - 60 = 40. Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct. - Set up a system of linear equations based on the problem statement. - One equation represents the total count of items. - Another equation represents the total value based on the count and individual item values. - Solve the system of equations using substitution or elimination to find the required variable.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-\u20b9-2-and-\u20b9-5-coins-if\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:35:26+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 person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If","description":"Let x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins. We are given two pieces of information: 1. The total number of coins is 100: x + y = 100 2. The total value of the coins is \u20b9 320: 2x + 5y = 320 We have a system of two linear equations with two variables. We want to find the value of x. From the first equation, we can express y as y = 100 - x. Substitute this into the second equation: 2x + 5(100 - x) = 320 2x + 500 - 5x = 320 500 - 3x = 320 500 - 320 = 3x 180 = 3x x = 180 \/ 3 = 60. So, there are 60 coins of \u20b9 2. If x = 60, then y = 100 - 60 = 40. Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct. - Set up a system of linear equations based on the problem statement. - One equation represents the total count of items. - Another equation represents the total value based on the count and individual item values. - Solve the system of equations using substitution or elimination to find the required variable.","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-person-has-a-total-of-100-coins-consisting-of-\u20b9-2-and-\u20b9-5-coins-if\/","og_locale":"en_US","og_type":"article","og_title":"A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If","og_description":"Let x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins. We are given two pieces of information: 1. The total number of coins is 100: x + y = 100 2. The total value of the coins is \u20b9 320: 2x + 5y = 320 We have a system of two linear equations with two variables. We want to find the value of x. From the first equation, we can express y as y = 100 - x. Substitute this into the second equation: 2x + 5(100 - x) = 320 2x + 500 - 5x = 320 500 - 3x = 320 500 - 320 = 3x 180 = 3x x = 180 \/ 3 = 60. So, there are 60 coins of \u20b9 2. If x = 60, then y = 100 - 60 = 40. Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct. - Set up a system of linear equations based on the problem statement. - One equation represents the total count of items. - Another equation represents the total value based on the count and individual item values. - Solve the system of equations using substitution or elimination to find the required variable.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-\u20b9-2-and-\u20b9-5-coins-if\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:35:26+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-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/","name":"A person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:35:26+00:00","dateModified":"2025-06-01T10:35:26+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let x be the number of \u20b9 2 coins and y be the number of \u20b9 5 coins. We are given two pieces of information: 1. The total number of coins is 100: x + y = 100 2. The total value of the coins is \u20b9 320: 2x + 5y = 320 We have a system of two linear equations with two variables. We want to find the value of x. From the first equation, we can express y as y = 100 - x. Substitute this into the second equation: 2x + 5(100 - x) = 320 2x + 500 - 5x = 320 500 - 3x = 320 500 - 320 = 3x 180 = 3x x = 180 \/ 3 = 60. So, there are 60 coins of \u20b9 2. If x = 60, then y = 100 - 60 = 40. Check the total value: 2(60) + 5(40) = 120 + 200 = 320. This is correct. - Set up a system of linear equations based on the problem statement. - One equation represents the total count of items. - Another equation represents the total value based on the count and individual item values. - Solve the system of equations using substitution or elimination to find the required variable.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-has-a-total-of-100-coins-consisting-of-%e2%82%b9-2-and-%e2%82%b9-5-coins-if\/#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 person has a total of 100 coins consisting of \u20b9 2 and \u20b9 5 coins. If"}]},{"@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\/90726","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=90726"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90726\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}