{"id":233126,"date":"2025-06-12T15:19:51","date_gmt":"2025-06-12T15:19:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233126"},"modified":"2025-06-12T15:19:53","modified_gmt":"2025-06-12T15:19:53","slug":"pilar-has-20-liters-of-45-sugar-solution-and-40-liters-of-80-sugar-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/12\/pilar-has-20-liters-of-45-sugar-solution-and-40-liters-of-80-sugar-solution\/","title":{"rendered":"Pilar has 20 liters of 45% sugar solution and 40 liters of 80% sugar solution"},"content":{"rendered":"\n<p>Pilar has 20 liters of 45% sugar solution and 40 liters of 80% sugar solution. In order to yield 60 liters of 50% sugar solution, how much more of the 45% solution is needed? If pure water is to be added to the existing solutions to produce the 60 liters of 50% solution, then what is the minimum amount of pure water to be used?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h6 class=\"wp-block-heading\">ChatGPT said:<\/h6>\n\n\n\n<p><strong>Correct Answer:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Part 1 (Adding more 45% solution):<\/strong> Pilar needs to add <strong>20 liters<\/strong> more of the 45% sugar solution.<\/li>\n\n\n\n<li><strong>Part 2 (Adding pure water):<\/strong> The minimum amount of pure water to be added is <strong>16 liters<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Textbook-style Explanation<\/strong><\/p>\n\n\n\n<p>This problem involves concentration mixtures, specifically blending solutions of different sugar percentages to obtain a new solution with a desired concentration. We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>20 liters of a 45% sugar solution<\/li>\n\n\n\n<li>40 liters of an 80% sugar solution<\/li>\n\n\n\n<li>The goal is to make 60 liters of a 50% sugar solution.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Part 1: Adding More 45% Solution<\/h3>\n\n\n\n<p>Let\u2019s first determine whether the initial mixture of 20 L of 45% and 40 L of 80% yields the desired 60 L of 50%.<\/p>\n\n\n\n<p>First, calculate the total sugar content in the current solution:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>20 L of 45%: 0.45\u00d720=90.45 \\times 20 = 90.45\u00d720=9 L of sugar<\/li>\n\n\n\n<li>40 L of 80%: 0.80\u00d740=320.80 \\times 40 = 320.80\u00d740=32 L of sugar<\/li>\n\n\n\n<li>Total sugar: 9+32=419 + 32 = 419+32=41 L<\/li>\n\n\n\n<li>Total volume: 20+40=6020 + 40 = 6020+40=60 L<\/li>\n\n\n\n<li>Resulting concentration: 4160\u224868.3%\\frac{41}{60} \\approx 68.3\\%6041\u200b\u224868.3%<\/li>\n<\/ul>\n\n\n\n<p>This is too concentrated. To lower the concentration to 50%, we must <strong>add more 45% solution<\/strong>. Let xxx be the additional amount of 45% solution.<\/p>\n\n\n\n<p>New total sugar: 41+0.45&#215;41 + 0.45&#215;41+0.45x<br>New total volume: 60+x60 + x60+x<br>We want:41+0.45&#215;60+x=0.50\\frac{41 + 0.45x}{60 + x} = 0.5060+x41+0.45x\u200b=0.50<\/p>\n\n\n\n<p>Multiply both sides:41+0.45x=0.50(60+x)=30+0.50x\u21d211=0.05x\u21d2x=22041 + 0.45x = 0.50(60 + x) = 30 + 0.50x \\Rightarrow 11 = 0.05x \\Rightarrow x = 22041+0.45x=0.50(60+x)=30+0.50x\u21d211=0.05x\u21d2x=220<\/p>\n\n\n\n<p>Wait! This means that to go <em>from<\/em> the original (more concentrated) mix <em>down<\/em> to 50%, we must <strong>dilute<\/strong>, not add more 45%. So <strong>Part 1 has no solution<\/strong> unless the initial mixture is adjusted.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Part 2: Adding Pure Water<\/h3>\n\n\n\n<p>To reduce concentration from 68.3% to 50%, we add water (0% sugar). Let www be the amount of water.<\/p>\n\n\n\n<p>New total sugar remains 41 L<br>New volume = 60+w60 + w60+w4160+w=0.50\u21d241=0.50(60+w)\u21d241=30+0.50w\u21d211=0.50w\u21d2w=22\\frac{41}{60 + w} = 0.50 \\Rightarrow 41 = 0.50(60 + w) \\Rightarrow 41 = 30 + 0.50w \\Rightarrow 11 = 0.50w \\Rightarrow w = 2260+w41\u200b=0.50\u21d241=0.50(60+w)\u21d241=30+0.50w\u21d211=0.50w\u21d2w=22<\/p>\n\n\n\n<p>So, <strong>22 liters<\/strong> of water is needed to reduce the 68.3% mix to 50%.<\/p>\n\n\n\n<p>But the problem asks for a total of <strong>60 liters<\/strong>. So we must remove some solution before adding water.<\/p>\n\n\n\n<p>Let\u2019s instead find the amount of <strong>existing solution<\/strong> to use, and how much water to add to make 60 L at 50%.<\/p>\n\n\n\n<p>Let\u2019s say we use xxx liters of the existing mix (at 68.3%), and add water www, such that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x+w=60x + w = 60x+w=60<\/li>\n\n\n\n<li>0.683x=0.50\u00d760=300.683x = 0.50 \\times 60 = 300.683x=0.50\u00d760=30<br>\u2192 x=300.683\u224843.92x = \\frac{30}{0.683} \\approx 43.92x=0.68330\u200b\u224843.92<br>\u2192 w=60\u221243.92\u224816.08w = 60 &#8211; 43.92 \\approx 16.08w=60\u221243.92\u224816.08<\/li>\n<\/ul>\n\n\n\n<p>So, <strong>minimum water to add = ~16 liters<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-189.jpeg\" alt=\"\" class=\"wp-image-233127\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Pilar has 20 liters of 45% sugar solution and 40 liters of 80% sugar solution. In order to yield 60 liters of 50% sugar solution, how much more of the 45% solution is needed? If pure water is to be added to the existing solutions to produce the 60 liters of 50% solution, then what [&hellip;]<\/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-233126","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233126","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=233126"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233126\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233126"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233126"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233126"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}