Q. An alloy of copper and zinc contains\u2026\u2026\u2026.% copper by weight. \u2018X\u2019 kg of zinc is added to the mixture which makes zinc 33 1\/3% by weight. If \u2018X\u2019 Kg of copper would have been added instead, the percentage of Cu by weight would be 83 1\/3%. If 3X Kgs zinc would have been added, the percentage of zinc will become\u2026\u2026\u2026\u2026The ratio of the weight of the original mixture to X is 5:1.<\/p>\n\n\n\n
A) 80%, 50%<\/strong><\/p>\n\n\n\n B) 50%, 80%<\/p>\n\n\n\n C) 75%, 60%<\/p>\n\n\n\n D) 60%, 75%<\/p>\n\n\n\n E) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Let the weight of copper and zinc be \u2018a\u2019 and \u2018b\u2019respectively.<\/p>\n\n\n\n X\u2019 kg of zinc is added to the mixture which makes zinc 33 1\/3% by weight<\/p>\n\n\n\n => (b+X)\/(a+b+X)=1\/3<\/p>\n\n\n\n => 3b+3X=a+b+X<\/p>\n\n\n\n => 2b=a-2X<\/p>\n\n\n\n => a=2b+2X —————————(1)<\/p>\n\n\n\n Again, if X Kg of copper would have been added<\/p>\n\n\n\n instead, the percentage of Cu by weight would<\/p>\n\n\n\n be 83 1\/3%.<\/p>\n\n\n\n => (a+X)\/(a+b+X)=5\/6<\/p>\n\n\n\n => 6a+6X=5a+5b+5X<\/p>\n\n\n\n => a=5b-X —————————(2)<\/p>\n\n\n\n Ratio of weight of original mixture and X is 5:1<\/p>\n\n\n\n => (a+b)\/X=5<\/p>\n\n\n\n =>a+b=5X<\/p>\n\n\n\n => a= 5X-b ——————————-(3)<\/p>\n\n\n\n Using (2) and (3), we get<\/p>\n\n\n\n 5b-X=5X-b<\/p>\n\n\n\n => 6b=6X<\/p>\n\n\n\n => b=X<\/p>\n\n\n\n From (1) and (2), we get<\/p>\n\n\n\n 2b+2X=5b-X<\/p>\n\n\n\n => 3b=3X<\/p>\n\n\n\n => b=X<\/p>\n\n\n\n From (3), we get<\/p>\n\n\n\n a=5b-b=4b<\/p>\n\n\n\n => a=4b<\/p>\n\n\n\n If 3X Kgs zinc would have been added,<\/p>\n\n\n\n Percentage of zinc=<\/p>\n\n\n\n (b+3X)\/(a+b+3X)*100%=(b+3b)\/(4b+b+3b)*100=<\/p>\n\n\n\n 4b\/8b*100%=<\/p>\n\n\n\n 50%<\/p>\n\n\n\n Also, initial weight of copper by<\/p>\n\n\n\n %=a\/(a+b)*100%=4b\/5b*100=80%<\/p>\n","protected":false},"excerpt":{"rendered":" Q. An alloy of copper and zinc contains\u2026\u2026\u2026.% copper by weight. \u2018X\u2019 kg of zinc is added to the mixture which makes zinc 33 1\/3% by weight. If \u2018X\u2019 Kg of copper would have been added instead, the percentage of Cu by weight would be 83 1\/3%. If 3X Kgs zinc would have been added, […]<\/p>\n","protected":false},"author":419,"featured_media":162986,"comment_status":"open","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-4)","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-4)","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-4)","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":[5138],"tags":[5139],"class_list":["post-162985","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-quantitative-aptitude","tag-quantitative-aptitude"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162985","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=162985"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162985\/revisions"}],"predecessor-version":[{"id":162987,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/162985\/revisions\/162987"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/162986"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=162985"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=162985"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=162985"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}