{"id":160980,"date":"2024-11-03T18:23:11","date_gmt":"2024-11-03T18:23:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=160980"},"modified":"2024-11-03T18:23:13","modified_gmt":"2024-11-03T18:23:13","slug":"p-and-q-are-two-numbers-such-that-pq","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/03\/p-and-q-are-two-numbers-such-that-pq\/","title":{"rendered":"p and q are two numbers such that p>q ."},"content":{"rendered":"\n

p and q are two numbers such that p>q .<\/p>\n\n\n\n

When you subtract 5 from p and subtract 5 from q , the answers are in the ratio 9:1. 2. When you add 20 to p and add 20 to q , the answers are in the ratio 7:3. Find the ratio p:q . Give your answer in its simplest form.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve for the ratio ( p:q ) based on the conditions provided, let’s denote the two numbers as ( p ) and ( q ).<\/p>\n\n\n\n

Given Conditions:<\/h3>\n\n\n\n
    \n
  1. Condition 1<\/strong>: When 5 is subtracted from both numbers, the result is in the ratio ( 9:1 ).
    [
    \\frac{p – 5}{q – 5} = \\frac{9}{1}
    ]
    This can be rewritten as:
    [
    p – 5 = 9(q – 5)
    ]
    Expanding this gives:
    [
    p – 5 = 9q – 45 \\implies p = 9q – 40 \\quad \\text{(Equation 1)}
    ]<\/li>\n\n\n\n
  2. Condition 2<\/strong>: When 20 is added to both numbers, the result is in the ratio ( 7:3 ).
    [
    \\frac{p + 20}{q + 20} = \\frac{7}{3}
    ]
    This can be rewritten as:
    [
    3(p + 20) = 7(q + 20)
    ]
    Expanding this gives:
    [
    3p + 60 = 7q + 140 \\implies 3p = 7q + 80 \\implies p = \\frac{7q + 80}{3} \\quad \\text{(Equation 2)}
    ]<\/li>\n<\/ol>\n\n\n\n

    Solving the Equations<\/h3>\n\n\n\n

    Now we have two equations:<\/p>\n\n\n\n

      \n
    • Equation 1: ( p = 9q – 40 )<\/li>\n\n\n\n
    • Equation 2: ( p = \\frac{7q + 80}{3} )<\/li>\n<\/ul>\n\n\n\n

      Setting these equal to each other:
      [
      9q – 40 = \\frac{7q + 80}{3}
      ]<\/p>\n\n\n\n

      To eliminate the fraction, multiply both sides by 3:
      [
      3(9q – 40) = 7q + 80
      ]
      Expanding gives:
      [
      27q – 120 = 7q + 80
      ]
      Now, isolate ( q ):
      [
      27q – 7q = 80 + 120 \\implies 20q = 200 \\implies q = 10
      ]<\/p>\n\n\n\n

      Finding ( p )<\/h3>\n\n\n\n

      Substituting ( q = 10 ) back into Equation 1 to find ( p ):
      [
      p = 9(10) – 40 = 90 – 40 = 50
      ]<\/p>\n\n\n\n

      Finding the Ratio<\/h3>\n\n\n\n

      Thus, we have:<\/p>\n\n\n\n

        \n
      • ( p = 50 )<\/li>\n\n\n\n
      • ( q = 10 )<\/li>\n<\/ul>\n\n\n\n

        Now, the ratio ( p:q ) is:
        [
        \\frac{p}{q} = \\frac{50}{10} = 5:1
        ]<\/p>\n\n\n\n

        Conclusion<\/h3>\n\n\n\n

        The simplest form of the ratio ( p:q ) is ( 5:1 ). This result is consistent with the conditions provided, confirming the solution is correct. Thus, the answer is:<\/p>\n\n\n\n

        [
        \\boxed{5:1}
        ]<\/p>\n\n\n\n

        In summary, the method involved setting up equations based on the conditions given, solving these simultaneous equations, and deriving the values of ( p ) and ( q ) to determine their ratio.<\/p>\n","protected":false},"excerpt":{"rendered":"

        p and q are two numbers such that p>q . When you subtract 5 from p and subtract 5 from q , the answers are in the ratio 9:1. 2. When you add 20 to p and add 20 to q , the answers are in the ratio 7:3. Find the ratio p:q . Give […]<\/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-160980","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160980","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=160980"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160980\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160980"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160980"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160980"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}