{"id":90683,"date":"2025-06-01T10:33:37","date_gmt":"2025-06-01T10:33:37","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90683"},"modified":"2025-06-01T10:33:37","modified_gmt":"2025-06-01T10:33:37","slug":"a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/","title":{"rendered":"A person buys an item from a shop for which the shopkeeper offers a di"},"content":{"rendered":"<p>A person buys an item from a shop for which the shopkeeper offers a discount of 10% on the marked price. The person pays using an e-wallet which gives 10% cash back. Which one of the following is the value of effective discount?<\/p>\n<p>[amp_mcq option1=&#8221;20%&#8221; option2=&#8221;18%&#8221; option3=&#8221;19%&#8221; option4=&#8221;21%&#8221; correct=&#8221;option3&#8243;]<\/p>\n<div class=\"psc-box-pyq-exam-year-detail\">\n<div class=\"pyq-exam\">\n<div class=\"psc-heading\">This question was previously asked in<\/div>\n<div class=\"psc-title line-ellipsis\">UPSC CAPF &#8211; 2022<\/div>\n<\/div>\n<div class=\"pyq-exam-psc-buttons\"><a href=\"\/pyq\/pyq-upsc-capf-2022.pdf\" target=\"_blank\" class=\"psc-pdf-button\" rel=\"noopener\">Download PDF<\/a><a href=\"\/pyq-upsc-capf-2022\" target=\"_blank\" class=\"psc-attempt-button\" rel=\"noopener\">Attempt Online<\/a><\/div>\n<\/div>\n<section id=\"pyq-correct-answer\">Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 \\times (1 &#8211; 0.10) = 100 \\times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 \\times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(\\frac{19}{100}) \\times 100\\% = 19\\%$.<\/section>\n<section id=\"pyq-key-points\">The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.<\/section>\n<section id=\"pyq-additional-information\">A common mistake is to simply add the percentages (10% + 10% = 20%), which is incorrect because the second percentage is applied to a reduced amount. This problem involves successive discounts\/benefits. If the marked price is M, the price paid is $M(1-d_1)$. The cashback is $C = M(1-d_1) \\times c$, where $d_1$ is the shop discount rate and $c$ is the cashback rate. The effective price paid is $M(1-d_1) &#8211; C = M(1-d_1) &#8211; M(1-d_1)c = M(1-d_1)(1-c)$. The total reduction is $M &#8211; M(1-d_1)(1-c)$. For this problem, it is $M &#8211; M(0.9)(0.9) = M &#8211; 0.81M = 0.19M$. The effective discount rate is $0.19 \\times 100\\% = 19\\%$.<\/section>\n","protected":false},"excerpt":{"rendered":"<p>A person buys an item from a shop for which the shopkeeper offers a discount of 10% on the marked price. The person pays using an e-wallet which gives 10% cash back. Which one of the following is the value of effective discount? [amp_mcq option1=&#8221;20%&#8221; option2=&#8221;18%&#8221; option3=&#8221;19%&#8221; option4=&#8221;21%&#8221; correct=&#8221;option3&#8243;] This question was previously asked in &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"A person buys an item from a shop for which the shopkeeper offers a di\" class=\"read-more button\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/#more-90683\">Detailed Solution<span class=\"screen-reader-text\">A person buys an item from a shop for which the shopkeeper offers a di<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1108,1102],"class_list":["post-90683","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A person buys an item from a shop for which the shopkeeper offers a di<\/title>\n<meta name=\"description\" content=\"Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 times (1 - 0.10) = 100 times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(frac{19}{100}) times 100% = 19%$. The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A person buys an item from a shop for which the shopkeeper offers a di\" \/>\n<meta property=\"og:description\" content=\"Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 times (1 - 0.10) = 100 times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(frac{19}{100}) times 100% = 19%$. The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:33:37+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"A person buys an item from a shop for which the shopkeeper offers a di","description":"Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 times (1 - 0.10) = 100 times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(frac{19}{100}) times 100% = 19%$. The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/","og_locale":"en_US","og_type":"article","og_title":"A person buys an item from a shop for which the shopkeeper offers a di","og_description":"Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 times (1 - 0.10) = 100 times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(frac{19}{100}) times 100% = 19%$. The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:33:37+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/","name":"A person buys an item from a shop for which the shopkeeper offers a di","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:33:37+00:00","dateModified":"2025-06-01T10:33:37+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 \\times (1 - 0.10) = 100 \\times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 \\times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(\\frac{19}{100}) \\times 100\\% = 19\\%$. The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-person-buys-an-item-from-a-shop-for-which-the-shopkeeper-offers-a-di\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"A person buys an item from a shop for which the shopkeeper offers a di"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90683","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90683"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90683\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90683"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90683"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90683"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}