{"id":93288,"date":"2025-06-01T11:46:39","date_gmt":"2025-06-01T11:46:39","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93288"},"modified":"2025-06-01T11:46:39","modified_gmt":"2025-06-01T11:46:39","slug":"in-a-game-between-x-and-y-x-has-to-give-%e2%82%b9-10-each-time-he-loses-to-y","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/in-a-game-between-x-and-y-x-has-to-give-%e2%82%b9-10-each-time-he-loses-to-y\/","title":{"rendered":"In a game between X and Y, X has to give \u20b9 10 each time he loses to Y."},"content":{"rendered":"

In a game between X and Y, X has to give \u20b9 10 each time he loses to Y. If he wins, then he gets \u20b9 50 from Y. If they play 15 times and X earns \u20b9 450, how many times does X win ?<\/p>\n

[amp_mcq option1=”8″ option2=”9″ option3=”10″ option4=”12″ correct=”option3″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X’s net earning is the total gain minus the total loss, which is 50W – 10L. We are given that X earns \u20b9 450, so 50W – 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W – 10L = 450. From equation 1, L = 15 – W. Substituting this into equation 2: 50W – 10(15 – W) = 450. 50W – 150 + 10W = 450. 60W – 150 = 450. 60W = 600. W = 600 \/ 60 = 10. X wins 10 times.
\n<\/section>\n
\n– Define variables for the number of wins and losses.
\n– Set up one equation based on the total number of games played.
\n– Set up a second equation based on the total net earning (total gain from wins minus total loss from losses).
\n– Solve the system of linear equations for the number of wins.
\n<\/section>\n
\nThis is an algebra word problem that requires setting up and solving a system of equations. It’s important to correctly represent the gain and loss per game and relate the total gain\/loss to the net earning. Checking the answer (10 wins, 5 losses: 10*50 – 5*10 = 500 – 50 = 450) confirms the solution.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

In a game between X and Y, X has to give \u20b9 10 each time he loses to Y. If he wins, then he gets \u20b9 50 from Y. If they play 15 times and X earns \u20b9 450, how many times does X win ? [amp_mcq option1=”8″ option2=”9″ option3=”10″ option4=”12″ correct=”option3″] This question was … <\/p>\n

Detailed SolutionIn a game between X and Y, X has to give \u20b9 10 each time he loses to Y.<\/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":[1105,1102],"class_list":["post-93288","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nIn a game between X and Y, X has to give \u20b9 10 each time he loses to Y.<\/title>\n<meta name=\"description\" content=\"Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X's net earning is the total gain minus the total loss, which is 50W - 10L. We are given that X earns \u20b9 450, so 50W - 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W - 10L = 450. From equation 1, L = 15 - W. Substituting this into equation 2: 50W - 10(15 - W) = 450. 50W - 150 + 10W = 450. 60W - 150 = 450. 60W = 600. W = 600 \/ 60 = 10. X wins 10 times. - Define variables for the number of wins and losses. - Set up one equation based on the total number of games played. - Set up a second equation based on the total net earning (total gain from wins minus total loss from losses). - Solve the system of linear equations for the number of wins.\" \/>\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\/in-a-game-between-x-and-y-x-has-to-give-\u20b9-10-each-time-he-loses-to-y\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"In a game between X and Y, X has to give \u20b9 10 each time he loses to Y.\" \/>\n<meta property=\"og:description\" content=\"Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X's net earning is the total gain minus the total loss, which is 50W - 10L. We are given that X earns \u20b9 450, so 50W - 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W - 10L = 450. From equation 1, L = 15 - W. Substituting this into equation 2: 50W - 10(15 - W) = 450. 50W - 150 + 10W = 450. 60W - 150 = 450. 60W = 600. W = 600 \/ 60 = 10. X wins 10 times. - Define variables for the number of wins and losses. - Set up one equation based on the total number of games played. - Set up a second equation based on the total net earning (total gain from wins minus total loss from losses). - Solve the system of linear equations for the number of wins.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/in-a-game-between-x-and-y-x-has-to-give-\u20b9-10-each-time-he-loses-to-y\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:46:39+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":"In a game between X and Y, X has to give \u20b9 10 each time he loses to Y.","description":"Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X's net earning is the total gain minus the total loss, which is 50W - 10L. We are given that X earns \u20b9 450, so 50W - 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W - 10L = 450. From equation 1, L = 15 - W. Substituting this into equation 2: 50W - 10(15 - W) = 450. 50W - 150 + 10W = 450. 60W - 150 = 450. 60W = 600. W = 600 \/ 60 = 10. X wins 10 times. - Define variables for the number of wins and losses. - Set up one equation based on the total number of games played. - Set up a second equation based on the total net earning (total gain from wins minus total loss from losses). - Solve the system of linear equations for the number of wins.","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\/in-a-game-between-x-and-y-x-has-to-give-\u20b9-10-each-time-he-loses-to-y\/","og_locale":"en_US","og_type":"article","og_title":"In a game between X and Y, X has to give \u20b9 10 each time he loses to Y.","og_description":"Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X's net earning is the total gain minus the total loss, which is 50W - 10L. We are given that X earns \u20b9 450, so 50W - 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W - 10L = 450. From equation 1, L = 15 - W. Substituting this into equation 2: 50W - 10(15 - W) = 450. 50W - 150 + 10W = 450. 60W - 150 = 450. 60W = 600. W = 600 \/ 60 = 10. X wins 10 times. - Define variables for the number of wins and losses. - Set up one equation based on the total number of games played. - Set up a second equation based on the total net earning (total gain from wins minus total loss from losses). - Solve the system of linear equations for the number of wins.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/in-a-game-between-x-and-y-x-has-to-give-\u20b9-10-each-time-he-loses-to-y\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:46:39+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\/in-a-game-between-x-and-y-x-has-to-give-%e2%82%b9-10-each-time-he-loses-to-y\/","url":"https:\/\/exam.pscnotes.com\/mcq\/in-a-game-between-x-and-y-x-has-to-give-%e2%82%b9-10-each-time-he-loses-to-y\/","name":"In a game between X and Y, X has to give \u20b9 10 each time he loses to Y.","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:46:39+00:00","dateModified":"2025-06-01T11:46:39+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let W be the number of times X wins and L be the number of times X loses. The total number of games played is W + L = 15. When X wins, he gains \u20b9 50, so the total gain from wins is 50W. When X loses, he gives \u20b9 10, so the total loss from losses is 10L. X's net earning is the total gain minus the total loss, which is 50W - 10L. We are given that X earns \u20b9 450, so 50W - 10L = 450. We now have a system of two linear equations: 1) W + L = 15 and 2) 50W - 10L = 450. From equation 1, L = 15 - W. Substituting this into equation 2: 50W - 10(15 - W) = 450. 50W - 150 + 10W = 450. 60W - 150 = 450. 60W = 600. W = 600 \/ 60 = 10. 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