{"id":90614,"date":"2025-06-01T10:32:10","date_gmt":"2025-06-01T10:32:10","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90614"},"modified":"2025-06-01T10:32:10","modified_gmt":"2025-06-01T10:32:10","slug":"the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/","title":{"rendered":"The ratio of monthly incomes of A and B is 7 : 10. The ratio of their"},"content":{"rendered":"

The ratio of monthly incomes of A and B is 7 : 10. The ratio of their expenditures is 2 : 3. If each of A and B saves \u20b9 1,000 per month, then what will be the monthly income of B?<\/p>\n

[amp_mcq option1=”\u20b9 9,000″ option2=”\u20b9 10,000″ option3=”\u20b9 15,000″ option4=”\u20b9 12,000″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nIf the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000.
\n<\/section>\n
\n– Let the monthly income of A be 7x and the monthly income of B be 10x.
\n– Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y.
\n– Savings = Income – Expenditure.
\n– For A: 7x – 2y = 1000 (Equation 1)
\n– For B: 10x – 3y = 1000 (Equation 2)
\n– We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y:
\n 3 * (7x – 2y) = 3 * 1000 => 21x – 6y = 3000
\n 2 * (10x – 3y) = 2 * 1000 => 20x – 6y = 2000
\n– Subtract the second new equation from the first new equation:
\n (21x – 6y) – (20x – 6y) = 3000 – 2000
\n 21x – 20x = 1000
\n x = 1000.
\n– The monthly income of B is 10x.
\n– Monthly income of B = 10 * 1000 = \u20b910,000.
\n<\/section>\n
\nWe can also find the incomes and expenditures:
\nIncome of A = 7 * 1000 = \u20b97,000
\nIncome of B = 10 * 1000 = \u20b910,000
\nSubstitute x=1000 into Equation 1: 7(1000) – 2y = 1000 => 7000 – 2y = 1000 => 2y = 6000 => y = 3000.
\nExpenditure of A = 2y = 2 * 3000 = \u20b96,000. Savings of A = 7000 – 6000 = \u20b91,000.
\nExpenditure of B = 3y = 3 * 3000 = \u20b99,000. Savings of B = 10000 – 9000 = \u20b91,000.
\nThe savings match the given information, confirming the value of x.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The ratio of monthly incomes of A and B is 7 : 10. The ratio of their expenditures is 2 : 3. If each of A and B saves \u20b9 1,000 per month, then what will be the monthly income of B? [amp_mcq option1=”\u20b9 9,000″ option2=”\u20b9 10,000″ option3=”\u20b9 15,000″ option4=”\u20b9 12,000″ correct=”option2″] This question was … <\/p>\n

Detailed SolutionThe ratio of monthly incomes of A and B is 7 : 10. The ratio of their<\/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":[1110,1102],"class_list":["post-90614","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1110","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe ratio of monthly incomes of A and B is 7 : 10. The ratio of their<\/title>\n<meta name=\"description\" content=\"If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000. - Let the monthly income of A be 7x and the monthly income of B be 10x. - Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y. - Savings = Income - Expenditure. - For A: 7x - 2y = 1000 (Equation 1) - For B: 10x - 3y = 1000 (Equation 2) - We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y: 3 * (7x - 2y) = 3 * 1000 => 21x - 6y = 3000 2 * (10x - 3y) = 2 * 1000 => 20x - 6y = 2000 - Subtract the second new equation from the first new equation: (21x - 6y) - (20x - 6y) = 3000 - 2000 21x - 20x = 1000 x = 1000. - The monthly income of B is 10x. - Monthly income of B = 10 * 1000 = \u20b910,000.\" \/>\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\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The ratio of monthly incomes of A and B is 7 : 10. The ratio of their\" \/>\n<meta property=\"og:description\" content=\"If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000. - Let the monthly income of A be 7x and the monthly income of B be 10x. - Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y. - Savings = Income - Expenditure. - For A: 7x - 2y = 1000 (Equation 1) - For B: 10x - 3y = 1000 (Equation 2) - We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y: 3 * (7x - 2y) = 3 * 1000 => 21x - 6y = 3000 2 * (10x - 3y) = 2 * 1000 => 20x - 6y = 2000 - Subtract the second new equation from the first new equation: (21x - 6y) - (20x - 6y) = 3000 - 2000 21x - 20x = 1000 x = 1000. - The monthly income of B is 10x. - Monthly income of B = 10 * 1000 = \u20b910,000.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:32:10+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=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The ratio of monthly incomes of A and B is 7 : 10. The ratio of their","description":"If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000. - Let the monthly income of A be 7x and the monthly income of B be 10x. - Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y. - Savings = Income - Expenditure. - For A: 7x - 2y = 1000 (Equation 1) - For B: 10x - 3y = 1000 (Equation 2) - We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y: 3 * (7x - 2y) = 3 * 1000 => 21x - 6y = 3000 2 * (10x - 3y) = 2 * 1000 => 20x - 6y = 2000 - Subtract the second new equation from the first new equation: (21x - 6y) - (20x - 6y) = 3000 - 2000 21x - 20x = 1000 x = 1000. - The monthly income of B is 10x. - Monthly income of B = 10 * 1000 = \u20b910,000.","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\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/","og_locale":"en_US","og_type":"article","og_title":"The ratio of monthly incomes of A and B is 7 : 10. The ratio of their","og_description":"If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000. - Let the monthly income of A be 7x and the monthly income of B be 10x. - Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y. - Savings = Income - Expenditure. - For A: 7x - 2y = 1000 (Equation 1) - For B: 10x - 3y = 1000 (Equation 2) - We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y: 3 * (7x - 2y) = 3 * 1000 => 21x - 6y = 3000 2 * (10x - 3y) = 2 * 1000 => 20x - 6y = 2000 - Subtract the second new equation from the first new equation: (21x - 6y) - (20x - 6y) = 3000 - 2000 21x - 20x = 1000 x = 1000. - The monthly income of B is 10x. - Monthly income of B = 10 * 1000 = \u20b910,000.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:32:10+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\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/","name":"The ratio of monthly incomes of A and B is 7 : 10. The ratio of their","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:32:10+00:00","dateModified":"2025-06-01T10:32:10+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves \u20b91,000 per month, the monthly income of B is \u20b910,000. - Let the monthly income of A be 7x and the monthly income of B be 10x. - Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y. - Savings = Income - Expenditure. - For A: 7x - 2y = 1000 (Equation 1) - For B: 10x - 3y = 1000 (Equation 2) - We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y: 3 * (7x - 2y) = 3 * 1000 => 21x - 6y = 3000 2 * (10x - 3y) = 2 * 1000 => 20x - 6y = 2000 - Subtract the second new equation from the first new equation: (21x - 6y) - (20x - 6y) = 3000 - 2000 21x - 20x = 1000 x = 1000. - The monthly income of B is 10x. - Monthly income of B = 10 * 1000 = \u20b910,000.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-ratio-of-monthly-incomes-of-a-and-b-is-7-10-the-ratio-of-their\/#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":"The ratio of monthly incomes of A and B is 7 : 10. 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