{"id":180880,"date":"2025-01-09T06:56:26","date_gmt":"2025-01-09T06:56:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=180880"},"modified":"2025-01-09T06:56:29","modified_gmt":"2025-01-09T06:56:29","slug":"when-i-was-2-my-sister-was-twice-my-age-now-im-40","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/09\/when-i-was-2-my-sister-was-twice-my-age-now-im-40\/","title":{"rendered":"When I was 2 my sister was twice my age Now I’m 40"},"content":{"rendered":"\n
    \n
  1. When I was 2 my sister was twice my age Now I’m 40, how old is my sister\u2026<\/li>\n\n\n\n
  2. Check all equations that are equivalent. A=(1)\/(2)h(b^(1)+b^(2)) 2A=hb^(1)+b^(2) b^(1)=(2A)\/(h)-b^(2) b^(1)=(2(A-(1)\/(2)hb^(2)))\/(h) RETRYV<\/li>\n<\/ol>\n\n\n\n

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

    1. How old is your sister when you are 40?<\/h3>\n\n\n\n

    When you were 2, your sister was twice your age, which means she was 4 years old at that time (since 2 * 2 = 4). The age difference between you and your sister is therefore 4 – 2 = 2 years.<\/p>\n\n\n\n

    Now that you are 40, your sister will be 40 + 2 = 42 years old<\/strong>.<\/p>\n\n\n\n

    2. Checking the Equivalence of Equations<\/h3>\n\n\n\n

    We need to check if the given equations are equivalent to the original equation:<\/p>\n\n\n\n

    Original equation:<\/h4>\n\n\n\n

    A=12h(b(1)+b(2))A = \\frac{1}{2} h \\left( b^{(1)} + b^{(2)} \\right)<\/p>\n\n\n\n

    Equation 1:<\/strong> 2A=hb(1)+b(2)2A = h b^{(1)} + b^{(2)}<\/p>\n\n\n\n

      \n
    • Multiply both sides of the original equation by 2: 2A=2\u22c512h(b(1)+b(2))=h(b(1)+b(2))2A = 2 \\cdot \\frac{1}{2} h \\left( b^{(1)} + b^{(2)} \\right) = h \\left( b^{(1)} + b^{(2)} \\right)<\/li>\n\n\n\n
    • This is not exactly the same as the given equation. In fact, it’s not possible to simplify to this form unless we disregard the grouping of terms (b^(1) + b^(2)) completely. So this equation is not equivalent<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Equation 2:<\/strong> b(1)=2Ah\u2212b(2)b^{(1)} = \\frac{2A}{h} – b^{(2)}<\/p>\n\n\n\n

        \n
      • Solving the original equation for b(1)b^{(1)}: A=12h(b(1)+b(2))A = \\frac{1}{2} h \\left( b^{(1)} + b^{(2)} \\right) Multiply both sides by 2: 2A=h(b(1)+b(2))2A = h \\left( b^{(1)} + b^{(2)} \\right) Subtract b(2)b^{(2)} from both sides: b(1)=2Ah\u2212b(2)b^{(1)} = \\frac{2A}{h} – b^{(2)}<\/li>\n\n\n\n
      • This matches the second equation perfectly. Therefore, this equation is equivalent<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Equation 3:<\/strong> b(1)=2(A\u221212hb(2))hb^{(1)} = \\frac{2 \\left( A – \\frac{1}{2} h b^{(2)} \\right)}{h}<\/p>\n\n\n\n

          \n
        • Start with the original equation: A=12h(b(1)+b(2))A = \\frac{1}{2} h \\left( b^{(1)} + b^{(2)} \\right) Solve for b(1)b^{(1)}: 2A=h(b(1)+b(2))2A = h \\left( b^{(1)} + b^{(2)} \\right) Subtract b(2)b^{(2)} from both sides: b(1)=2Ah\u2212b(2)b^{(1)} = \\frac{2A}{h} – b^{(2)}<\/li>\n\n\n\n
        • Now substitute: b(1)=2(A\u221212hb(2))hb^{(1)} = \\frac{2 \\left( A – \\frac{1}{2} h b^{(2)} \\right)}{h}<\/li>\n\n\n\n
        • Expanding this: b(1)=2Ah\u2212b(2)b^{(1)} = \\frac{2A}{h} – b^{(2)}<\/li>\n\n\n\n
        • This matches the second equation exactly, so this equation is equivalent<\/strong> as well.<\/li>\n<\/ul>\n\n\n\n

          Summary:<\/h3>\n\n\n\n
            \n
          • The second and third equations are equivalent<\/strong> to the original one.<\/li>\n\n\n\n
          • The first equation is not equivalent<\/strong>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

            The Correct Answer and Explanation is : 1. How old is your sister when you are 40? When you were 2, your sister was twice your age, which means she was 4 years old at that time (since 2 * 2 = 4). The age difference between you and your sister is therefore 4 – […]<\/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-180880","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180880","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=180880"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/180880\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=180880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=180880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=180880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}