{"id":90238,"date":"2025-06-01T10:23:41","date_gmt":"2025-06-01T10:23:41","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90238"},"modified":"2025-06-01T10:23:41","modified_gmt":"2025-06-01T10:23:41","slug":"a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/","title":{"rendered":"A king ordered to make a crown from 8 kg of gold and 2 kg of silver. T"},"content":{"rendered":"

A king ordered to make a crown from 8 kg of gold and 2 kg of silver. The goldsmith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. The king knows that under water gold loses $\\frac{1}{20}$th of its weight, while silver loses $\\frac{1}{10}$th. When the crown was weighed under water, it was 9.25 kg. How much gold was stolen by the goldsmith?<\/p>\n

[amp_mcq option1=”1 kg” option2=”2 kg” option3=”3 kg” option4=”4 kg” correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is C) 3 kg.
\n<\/section>\n
\nInitial composition: 8 kg gold, 2 kg silver, total 10 kg.
\nLet ‘x’ kg of gold be stolen and replaced by ‘x’ kg of silver.
\nFinal composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg.
\nUnder water, gold loses 1\/20th of its weight, so its apparent weight is (1 – 1\/20) = 19\/20 of its actual weight.
\nUnder water, silver loses 1\/10th of its weight, so its apparent weight is (1 – 1\/10) = 9\/10 of its actual weight.
\nThe crown weighs 9.25 kg under water.
\nApparent weight of gold = (19\/20) * (8-x)
\nApparent weight of silver = (9\/10) * (2+x)
\nTotal apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25
\nMultiply by 20 to clear the denominators:
\n19 * (8-x) + 18 * (2+x) = 9.25 * 20
\n152 – 19x + 36 + 18x = 185
\n188 – x = 185
\nx = 188 – 185
\nx = 3 kg.
\nThe goldsmith stole 3 kg of gold.
\n<\/section>\n
\nThis problem is an application of Archimedes’ principle. The weight loss under water is equal to the weight of the water displaced, which is proportional to the volume of the object. Different densities of gold and silver cause different weight losses for the same weight. Pure gold is much denser than silver, so 1 kg of gold occupies less volume than 1 kg of silver and displaces less water, thus losing less weight. Replacing gold with silver increases the overall volume for the same weight, leading to a greater weight loss under water. The initial weight loss for the pure crown would have been (1\/20)*8 + (1\/10)*2 = 0.4 + 0.2 = 0.6 kg, making its underwater weight 10 – 0.6 = 9.4 kg. The actual underwater weight is 9.25 kg, a loss of 0.75 kg (10 – 9.25). The increased loss of 0.15 kg (0.75 – 0.6) is due to the replacement of ‘x’ kg of gold with ‘x’ kg of silver. The difference in weight loss per kg is (1\/10) – (1\/20) = 1\/20. So, the increased loss is (1\/20)*x = 0.15 kg. x = 0.15 * 20 = 3 kg.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A king ordered to make a crown from 8 kg of gold and 2 kg of silver. The goldsmith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. The king knows that under water gold loses $\\frac{1}{20}$th of its weight, while … <\/p>\n

Detailed SolutionA king ordered to make a crown from 8 kg of gold and 2 kg of silver. T<\/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":[1114,1102],"class_list":["post-90238","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA king ordered to make a crown from 8 kg of gold and 2 kg of silver. T<\/title>\n<meta name=\"description\" content=\"The correct answer is C) 3 kg. Initial composition: 8 kg gold, 2 kg silver, total 10 kg. Let 'x' kg of gold be stolen and replaced by 'x' kg of silver. Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg. Under water, gold loses 1\/20th of its weight, so its apparent weight is (1 - 1\/20) = 19\/20 of its actual weight. Under water, silver loses 1\/10th of its weight, so its apparent weight is (1 - 1\/10) = 9\/10 of its actual weight. The crown weighs 9.25 kg under water. Apparent weight of gold = (19\/20) * (8-x) Apparent weight of silver = (9\/10) * (2+x) Total apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25 Multiply by 20 to clear the denominators: 19 * (8-x) + 18 * (2+x) = 9.25 * 20 152 - 19x + 36 + 18x = 185 188 - x = 185 x = 188 - 185 x = 3 kg. The goldsmith stole 3 kg of gold.\" \/>\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-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A king ordered to make a crown from 8 kg of gold and 2 kg of silver. T\" \/>\n<meta property=\"og:description\" content=\"The correct answer is C) 3 kg. Initial composition: 8 kg gold, 2 kg silver, total 10 kg. Let 'x' kg of gold be stolen and replaced by 'x' kg of silver. Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg. Under water, gold loses 1\/20th of its weight, so its apparent weight is (1 - 1\/20) = 19\/20 of its actual weight. Under water, silver loses 1\/10th of its weight, so its apparent weight is (1 - 1\/10) = 9\/10 of its actual weight. The crown weighs 9.25 kg under water. Apparent weight of gold = (19\/20) * (8-x) Apparent weight of silver = (9\/10) * (2+x) Total apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25 Multiply by 20 to clear the denominators: 19 * (8-x) + 18 * (2+x) = 9.25 * 20 152 - 19x + 36 + 18x = 185 188 - x = 185 x = 188 - 185 x = 3 kg. The goldsmith stole 3 kg of gold.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:23:41+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":"A king ordered to make a crown from 8 kg of gold and 2 kg of silver. T","description":"The correct answer is C) 3 kg. Initial composition: 8 kg gold, 2 kg silver, total 10 kg. Let 'x' kg of gold be stolen and replaced by 'x' kg of silver. Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg. Under water, gold loses 1\/20th of its weight, so its apparent weight is (1 - 1\/20) = 19\/20 of its actual weight. Under water, silver loses 1\/10th of its weight, so its apparent weight is (1 - 1\/10) = 9\/10 of its actual weight. The crown weighs 9.25 kg under water. Apparent weight of gold = (19\/20) * (8-x) Apparent weight of silver = (9\/10) * (2+x) Total apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25 Multiply by 20 to clear the denominators: 19 * (8-x) + 18 * (2+x) = 9.25 * 20 152 - 19x + 36 + 18x = 185 188 - x = 185 x = 188 - 185 x = 3 kg. The goldsmith stole 3 kg of gold.","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-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/","og_locale":"en_US","og_type":"article","og_title":"A king ordered to make a crown from 8 kg of gold and 2 kg of silver. T","og_description":"The correct answer is C) 3 kg. Initial composition: 8 kg gold, 2 kg silver, total 10 kg. Let 'x' kg of gold be stolen and replaced by 'x' kg of silver. Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg. Under water, gold loses 1\/20th of its weight, so its apparent weight is (1 - 1\/20) = 19\/20 of its actual weight. Under water, silver loses 1\/10th of its weight, so its apparent weight is (1 - 1\/10) = 9\/10 of its actual weight. The crown weighs 9.25 kg under water. Apparent weight of gold = (19\/20) * (8-x) Apparent weight of silver = (9\/10) * (2+x) Total apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25 Multiply by 20 to clear the denominators: 19 * (8-x) + 18 * (2+x) = 9.25 * 20 152 - 19x + 36 + 18x = 185 188 - x = 185 x = 188 - 185 x = 3 kg. The goldsmith stole 3 kg of gold.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:23:41+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\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/","name":"A king ordered to make a crown from 8 kg of gold and 2 kg of silver. T","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:23:41+00:00","dateModified":"2025-06-01T10:23:41+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is C) 3 kg. Initial composition: 8 kg gold, 2 kg silver, total 10 kg. Let 'x' kg of gold be stolen and replaced by 'x' kg of silver. Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg. Under water, gold loses 1\/20th of its weight, so its apparent weight is (1 - 1\/20) = 19\/20 of its actual weight. Under water, silver loses 1\/10th of its weight, so its apparent weight is (1 - 1\/10) = 9\/10 of its actual weight. The crown weighs 9.25 kg under water. Apparent weight of gold = (19\/20) * (8-x) Apparent weight of silver = (9\/10) * (2+x) Total apparent weight = (19\/20) * (8-x) + (9\/10) * (2+x) = 9.25 Multiply by 20 to clear the denominators: 19 * (8-x) + 18 * (2+x) = 9.25 * 20 152 - 19x + 36 + 18x = 185 188 - x = 185 x = 188 - 185 x = 3 kg. The goldsmith stole 3 kg of gold.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-king-ordered-to-make-a-crown-from-8-kg-of-gold-and-2-kg-of-silver-t\/#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 king ordered to make a crown from 8 kg of gold and 2 kg of silver. 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