{"id":224412,"date":"2025-06-03T05:46:55","date_gmt":"2025-06-03T05:46:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224412"},"modified":"2025-06-03T05:46:57","modified_gmt":"2025-06-03T05:46:57","slug":"given-that-a-b-c-75-120-132","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/given-that-a-b-c-75-120-132\/","title":{"rendered":"Given that a : b : c = 75 : 120 : 132"},"content":{"rendered":"\n
Given that a : b : c = 75 : 120 : 132,. simplify a : b : c,. find b : a,. find b : c with full explanation and simplification ( if used)<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
We are given the ratio: a:b:c=75:120:132a : b : c = 75 : 120 : 132<\/p>\n\n\n\n
\n\n\n\n
Step 1: Simplify the ratio a : b : c<\/strong><\/h3>\n\n\n\n
To simplify a ratio, we divide all parts of the ratio by their greatest common divisor (GCD)<\/strong>.<\/p>\n\n\n\n
Find the GCD of 75, 120, and 132:<\/strong><\/p>\n\n\n\n
\n
Prime factors of 75: 3\u00d7523 \\times 5^2<\/li>\n\n\n\n
Prime factors of 120: 23\u00d73\u00d752^3 \\times 3 \\times 5<\/li>\n\n\n\n
Prime factors of 132: 22\u00d73\u00d7112^2 \\times 3 \\times 11<\/li>\n<\/ul>\n\n\n\n
The common factor<\/strong> in all three numbers is 3<\/strong>.<\/p>\n\n\n\n
So, divide each part by 3<\/strong>: 753:1203:1323=25:40:44\\frac{75}{3} : \\frac{120}{3} : \\frac{132}{3} = 25 : 40 : 44<\/p>\n\n\n\n\n\n\n\n
Final Simplified Ratio:<\/strong><\/h3>\n\n\n\n
a:b:c=25:40:44a : b : c = 25 : 40 : 44<\/p>\n\n\n\n
\n\n\n\n
Step 2: Find b : a<\/strong><\/h3>\n\n\n\n
From the simplified ratio: a:b=25:40\u21d2b:a=40:25a : b = 25 : 40 \\Rightarrow b : a = 40 : 25<\/p>\n\n\n\n
Ratios are a way of comparing quantities relative to each other. In the problem, we are given the ratio a:b:c=75:120:132a : b : c = 75 : 120 : 132. This is a compound ratio involving three parts. To work with such a ratio, the first step is to simplify it, just as we would simplify a fraction.<\/p>\n\n\n\n
To simplify the three-part ratio, we find the greatest common divisor (GCD) of the three numbers. The GCD of 75, 120, and 132 is 3, since all three numbers share 3 as their highest common factor. Dividing each term by 3, we get the simplified ratio: 25:40:4425 : 40 : 44. This tells us that for every 25 units of a, there are 40 units of b and 44 units of c.<\/p>\n\n\n\n
Next, to find the ratio of b to a<\/strong>, we reverse the order of a : b and write it as b : a, which becomes 40:2540 : 25. To simplify, we divide both numbers by their GCD, which is 5, giving us 8:58 : 5.<\/p>\n\n\n\n
To find the ratio of b to c<\/strong>, we use the values from the simplified form: b:c=40:44b : c = 40 : 44. Their GCD is 4, so simplifying gives 10:1110 : 11.<\/p>\n\n\n\n
Understanding and simplifying ratios helps us compare different quantities efficiently. It is widely used in real-life contexts such as mixing ingredients, budgeting, and scaling measurements in science and engineering.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Given that a : b : c = 75 : 120 : 132,. simplify a : b : c,. find b : a,. find b : c with full explanation and simplification ( if used) The Correct Answer and Explanation is: We are given the ratio: a:b:c=75:120:132a : b : c = 75 : 120 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-224412","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224412","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224412"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224412\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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