{"id":92633,"date":"2025-06-01T11:29:32","date_gmt":"2025-06-01T11:29:32","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92633"},"modified":"2025-06-01T11:29:32","modified_gmt":"2025-06-01T11:29:32","slug":"i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/","title":{"rendered":"I had bought a shirt at 10% discount which I sold to a friend at a los"},"content":{"rendered":"

I had bought a shirt at 10% discount which I sold to a friend at a loss of 10%. If the friend paid me \u20b9729-00 for the shirt, what was the undiscounted price of the shirt?<\/p>\n

[amp_mcq option1=”\u20b9800″ option2=”\u20b9900″ option3=”\u20b9911-25″ option4=”\u20b91,000″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nLet the undiscounted price of the shirt be U.
\nThe shirt was bought at a 10% discount. So, the cost price (price I bought it for) is:
\nCost Price (CP) = U – 10% of U = U – 0.10U = 0.90U.<\/p>\n

I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP).
\nThe friend paid \u20b9729-00. This is the selling price (SP).
\nThe loss is calculated on the CP.
\nLoss = 10% of CP = 0.10 * CP.
\nSelling Price (SP) = CP – Loss = CP – 0.10 * CP = 0.90 * CP.<\/p>\n

We are given that the friend paid \u20b9729, so SP = \u20b9729.
\n729 = 0.90 * CP
\nTo find CP, divide 729 by 0.90:
\nCP = 729 \/ 0.9 = 7290 \/ 9 = 810.
\nSo, the cost price (the price I bought the shirt for) was \u20b9810.<\/p>\n

Now, we need to find the undiscounted price U, knowing that CP = 0.90U.
\n810 = 0.90 * U
\nTo find U, divide 810 by 0.90:
\nU = 810 \/ 0.9 = 8100 \/ 9 = 900.
\nThe undiscounted price of the shirt was \u20b9900.<\/p>\n

Let’s verify:
\nUndiscounted price = \u20b9900.
\n10% discount = 10% of 900 = 0.10 * 900 = \u20b990.
\nPrice after discount (CP) = 900 – 90 = \u20b9810. (This is the price I bought it for).
\nSold at a loss of 10% on CP:
\nLoss amount = 10% of 810 = 0.10 * 810 = \u20b981.
\nSelling Price (SP) = CP – Loss amount = 810 – 81 = \u20b9729.
\nThis matches the amount the friend paid.
\n<\/section>\n

\n– Discount is calculated on the original\/undiscounted price.
\n– Loss is calculated on the cost price (the price at which the seller bought the item).
\n– Selling Price = Cost Price – Loss.
\n– If something is sold at X% discount, the selling price is (100-X)% of the original price.
\n– If something is sold at Y% loss, the selling price is (100-Y)% of the cost price.
\n<\/section>\n
\nPercentage calculations require careful attention to the base amount (e.g., discount on original price, profit\/loss on cost price). Using decimal multipliers (like 0.90 for a 10% discount\/loss) can simplify calculations.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

I had bought a shirt at 10% discount which I sold to a friend at a loss of 10%. If the friend paid me \u20b9729-00 for the shirt, what was the undiscounted price of the shirt? [amp_mcq option1=”\u20b9800″ option2=”\u20b9900″ option3=”\u20b9911-25″ option4=”\u20b91,000″ correct=”option2″] This question was previously asked in UPSC CISF-AC-EXE – 2019 Download PDFAttempt Online … <\/p>\n

Detailed SolutionI had bought a shirt at 10% discount which I sold to a friend at a los<\/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":[1089],"tags":[1119,1102],"class_list":["post-92633","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1119","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nI had bought a shirt at 10% discount which I sold to a friend at a los<\/title>\n<meta name=\"description\" content=\"Let the undiscounted price of the shirt be U. The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is: Cost Price (CP) = U - 10% of U = U - 0.10U = 0.90U. I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP). The friend paid \u20b9729-00. This is the selling price (SP). The loss is calculated on the CP. Loss = 10% of CP = 0.10 * CP. Selling Price (SP) = CP - Loss = CP - 0.10 * CP = 0.90 * CP. We are given that the friend paid \u20b9729, so SP = \u20b9729. 729 = 0.90 * CP To find CP, divide 729 by 0.90: CP = 729 \/ 0.9 = 7290 \/ 9 = 810. So, the cost price (the price I bought the shirt for) was \u20b9810. Now, we need to find the undiscounted price U, knowing that CP = 0.90U. 810 = 0.90 * U To find U, divide 810 by 0.90: U = 810 \/ 0.9 = 8100 \/ 9 = 900. The undiscounted price of the shirt was \u20b9900. Let's verify: Undiscounted price = \u20b9900. 10% discount = 10% of 900 = 0.10 * 900 = \u20b990. Price after discount (CP) = 900 - 90 = \u20b9810. (This is the price I bought it for). Sold at a loss of 10% on CP: Loss amount = 10% of 810 = 0.10 * 810 = \u20b981. Selling Price (SP) = CP - Loss amount = 810 - 81 = \u20b9729. This matches the amount the friend paid. - Discount is calculated on the original\/undiscounted price. - Loss is calculated on the cost price (the price at which the seller bought the item). - Selling Price = Cost Price - Loss. - If something is sold at X% discount, the selling price is (100-X)% of the original price. - If something is sold at Y% loss, the selling price is (100-Y)% of the cost 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\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"I had bought a shirt at 10% discount which I sold to a friend at a los\" \/>\n<meta property=\"og:description\" content=\"Let the undiscounted price of the shirt be U. The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is: Cost Price (CP) = U - 10% of U = U - 0.10U = 0.90U. I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP). The friend paid \u20b9729-00. This is the selling price (SP). The loss is calculated on the CP. Loss = 10% of CP = 0.10 * CP. Selling Price (SP) = CP - Loss = CP - 0.10 * CP = 0.90 * CP. We are given that the friend paid \u20b9729, so SP = \u20b9729. 729 = 0.90 * CP To find CP, divide 729 by 0.90: CP = 729 \/ 0.9 = 7290 \/ 9 = 810. So, the cost price (the price I bought the shirt for) was \u20b9810. Now, we need to find the undiscounted price U, knowing that CP = 0.90U. 810 = 0.90 * U To find U, divide 810 by 0.90: U = 810 \/ 0.9 = 8100 \/ 9 = 900. The undiscounted price of the shirt was \u20b9900. Let's verify: Undiscounted price = \u20b9900. 10% discount = 10% of 900 = 0.10 * 900 = \u20b990. Price after discount (CP) = 900 - 90 = \u20b9810. (This is the price I bought it for). Sold at a loss of 10% on CP: Loss amount = 10% of 810 = 0.10 * 810 = \u20b981. Selling Price (SP) = CP - Loss amount = 810 - 81 = \u20b9729. This matches the amount the friend paid. - Discount is calculated on the original\/undiscounted price. - Loss is calculated on the cost price (the price at which the seller bought the item). - Selling Price = Cost Price - Loss. - If something is sold at X% discount, the selling price is (100-X)% of the original price. - If something is sold at Y% loss, the selling price is (100-Y)% of the cost price.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:29:32+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"I had bought a shirt at 10% discount which I sold to a friend at a los","description":"Let the undiscounted price of the shirt be U. The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is: Cost Price (CP) = U - 10% of U = U - 0.10U = 0.90U. I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP). The friend paid \u20b9729-00. This is the selling price (SP). The loss is calculated on the CP. Loss = 10% of CP = 0.10 * CP. Selling Price (SP) = CP - Loss = CP - 0.10 * CP = 0.90 * CP. We are given that the friend paid \u20b9729, so SP = \u20b9729. 729 = 0.90 * CP To find CP, divide 729 by 0.90: CP = 729 \/ 0.9 = 7290 \/ 9 = 810. So, the cost price (the price I bought the shirt for) was \u20b9810. Now, we need to find the undiscounted price U, knowing that CP = 0.90U. 810 = 0.90 * U To find U, divide 810 by 0.90: U = 810 \/ 0.9 = 8100 \/ 9 = 900. The undiscounted price of the shirt was \u20b9900. Let's verify: Undiscounted price = \u20b9900. 10% discount = 10% of 900 = 0.10 * 900 = \u20b990. Price after discount (CP) = 900 - 90 = \u20b9810. (This is the price I bought it for). Sold at a loss of 10% on CP: Loss amount = 10% of 810 = 0.10 * 810 = \u20b981. Selling Price (SP) = CP - Loss amount = 810 - 81 = \u20b9729. This matches the amount the friend paid. - Discount is calculated on the original\/undiscounted price. - Loss is calculated on the cost price (the price at which the seller bought the item). - Selling Price = Cost Price - Loss. - If something is sold at X% discount, the selling price is (100-X)% of the original price. - If something is sold at Y% loss, the selling price is (100-Y)% of the cost 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\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/","og_locale":"en_US","og_type":"article","og_title":"I had bought a shirt at 10% discount which I sold to a friend at a los","og_description":"Let the undiscounted price of the shirt be U. The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is: Cost Price (CP) = U - 10% of U = U - 0.10U = 0.90U. I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP). The friend paid \u20b9729-00. This is the selling price (SP). The loss is calculated on the CP. Loss = 10% of CP = 0.10 * CP. Selling Price (SP) = CP - Loss = CP - 0.10 * CP = 0.90 * CP. We are given that the friend paid \u20b9729, so SP = \u20b9729. 729 = 0.90 * CP To find CP, divide 729 by 0.90: CP = 729 \/ 0.9 = 7290 \/ 9 = 810. So, the cost price (the price I bought the shirt for) was \u20b9810. Now, we need to find the undiscounted price U, knowing that CP = 0.90U. 810 = 0.90 * U To find U, divide 810 by 0.90: U = 810 \/ 0.9 = 8100 \/ 9 = 900. The undiscounted price of the shirt was \u20b9900. Let's verify: Undiscounted price = \u20b9900. 10% discount = 10% of 900 = 0.10 * 900 = \u20b990. Price after discount (CP) = 900 - 90 = \u20b9810. (This is the price I bought it for). Sold at a loss of 10% on CP: Loss amount = 10% of 810 = 0.10 * 810 = \u20b981. Selling Price (SP) = CP - Loss amount = 810 - 81 = \u20b9729. This matches the amount the friend paid. - Discount is calculated on the original\/undiscounted price. - Loss is calculated on the cost price (the price at which the seller bought the item). - Selling Price = Cost Price - Loss. - If something is sold at X% discount, the selling price is (100-X)% of the original price. - If something is sold at Y% loss, the selling price is (100-Y)% of the cost price.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:29:32+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/","url":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/","name":"I had bought a shirt at 10% discount which I sold to a friend at a los","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:29:32+00:00","dateModified":"2025-06-01T11:29:32+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the undiscounted price of the shirt be U. The shirt was bought at a 10% discount. So, the cost price (price I bought it for) is: Cost Price (CP) = U - 10% of U = U - 0.10U = 0.90U. I sold this shirt to a friend at a loss of 10% on the price I bought it for (the CP). The friend paid \u20b9729-00. This is the selling price (SP). The loss is calculated on the CP. Loss = 10% of CP = 0.10 * CP. Selling Price (SP) = CP - Loss = CP - 0.10 * CP = 0.90 * CP. We are given that the friend paid \u20b9729, so SP = \u20b9729. 729 = 0.90 * CP To find CP, divide 729 by 0.90: CP = 729 \/ 0.9 = 7290 \/ 9 = 810. So, the cost price (the price I bought the shirt for) was \u20b9810. Now, we need to find the undiscounted price U, knowing that CP = 0.90U. 810 = 0.90 * U To find U, divide 810 by 0.90: U = 810 \/ 0.9 = 8100 \/ 9 = 900. The undiscounted price of the shirt was \u20b9900. Let's verify: Undiscounted price = \u20b9900. 10% discount = 10% of 900 = 0.10 * 900 = \u20b990. Price after discount (CP) = 900 - 90 = \u20b9810. (This is the price I bought it for). Sold at a loss of 10% on CP: Loss amount = 10% of 810 = 0.10 * 810 = \u20b981. Selling Price (SP) = CP - Loss amount = 810 - 81 = \u20b9729. This matches the amount the friend paid. - Discount is calculated on the original\/undiscounted price. - Loss is calculated on the cost price (the price at which the seller bought the item). - Selling Price = Cost Price - Loss. - If something is sold at X% discount, the selling price is (100-X)% of the original price. - If something is sold at Y% loss, the selling price is (100-Y)% of the cost price.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/i-had-bought-a-shirt-at-10-discount-which-i-sold-to-a-friend-at-a-los\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"I had bought a shirt at 10% discount which I sold to a friend at a los"}]},{"@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\/92633","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=92633"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92633\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}