{"id":2051,"date":"2024-03-05T15:27:07","date_gmt":"2024-03-05T15:27:07","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=2051"},"modified":"2024-03-05T15:27:07","modified_gmt":"2024-03-05T15:27:07","slug":"the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/","title":{"rendered":"The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?"},"content":{"rendered":"<p>[amp_mcq option1=&#8221;20&#8243; option2=&#8221;24&#8243; option3=&#8221;25&#8243; option4=&#8221;30&#8243; correct=&#8221;option2&#8243;]<!--more--><\/p>\n<p>The correct answer is (b).<\/p>\n<p>Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 \\times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = \\frac{162.5 &#8211; 15 \\times 6}{6} = 24$.<\/p>\n<p>Option (a) is incorrect because 20 students would give an average age of 15 years and 3 months, which is not 6 months less than the original average age. Option (c) is incorrect because 25 students would give an average age of 15 years and 1 month, which is not 6 months less than the original average age. Option (d) is incorrect because 30 students would give an average age of 15 years, which is not 6 months less than the original average age.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>[amp_mcq option1=&#8221;20&#8243; option2=&#8221;24&#8243; option3=&#8221;25&#8243; option4=&#8221;30&#8243; correct=&#8221;option2&#8243;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[33],"tags":[],"class_list":["post-2051","post","type-post","status-publish","format-standard","hentry","category-algebra","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?<\/title>\n<meta name=\"description\" content=\"Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = frac{162.5 - 15 times 6}{6} = 24$.\" \/>\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-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?\" \/>\n<meta property=\"og:description\" content=\"Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = frac{162.5 - 15 times 6}{6} = 24$.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-05T15:27:07+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 average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?","description":"Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = frac{162.5 - 15 times 6}{6} = 24$.","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-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/","og_locale":"en_US","og_type":"article","og_title":"The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?","og_description":"Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = frac{162.5 - 15 times 6}{6} = 24$.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2024-03-05T15:27:07+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-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/","name":"The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. How many students were there in the class originally?","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2024-03-05T15:27:07+00:00","dateModified":"2024-03-05T15:27:07+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let $x$ be the number of students in the class originally. The total age of the students in the class originally is $15x$ years. When 5 boys whose average age is 12 years and 6 months are admitted in the class, the total age of the students in the class is $15x + 5 \\times 12.5 = 162.5$ years. The average age of the students in the class is now 15 years and 6 months, which is 6 months less than the original average age. This means that the total number of students in the class has increased by 5. Therefore, $x = \\frac{162.5 - 15 \\times 6}{6} = 24$.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-average-age-of-a-class-was-15-years-when-5-boys-whose-average-age-was-12-years-and-6-months-were-admitted-in-the-class-the-average-was-reduced-to-6-months-how-many-students-were-there-in-the-cl\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"mcq","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/"},{"@type":"ListItem","position":3,"name":"Algebra","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/mcq\/algebra\/"},{"@type":"ListItem","position":4,"name":"The average age of a class was 15 years. When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months. 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