{"id":92524,"date":"2025-06-01T11:27:19","date_gmt":"2025-06-01T11:27:19","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92524"},"modified":"2025-06-01T11:27:19","modified_gmt":"2025-06-01T11:27:19","slug":"25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/","title":{"rendered":"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge"},"content":{"rendered":"

25 writers, 20 doctors, 18 dentists and 12 bank employees spent altogether \u20b9 1,330 in a hotel. However, it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists, and that 6 dentists spent as much as 8 bank employees. Out of the four professional groups, which group spent the maximum amount ?<\/p>\n

[amp_mcq option1=”Bank employees” option2=”Dentists” option3=”Doctors” option4=”Writers” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is B) Dentists.
\n<\/section>\n
\nLet $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees.
\nWe are given the following relationships:
\n1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s \\implies w_s = \\frac{4}{5}d_s$
\n2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s \\implies 4d_s = 3t_s \\implies t_s = \\frac{4}{3}d_s$
\n3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s \\implies 3t_s = 4b_s$
\nSubstitute $t_s$ from (2) into (3): $3(\\frac{4}{3}d_s) = 4b_s \\implies 4d_s = 4b_s \\implies d_s = b_s$
\nSo, we have $w_s = \\frac{4}{5}d_s$, $t_s = \\frac{4}{3}d_s$, and $b_s = d_s$.
\nThe total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$
\nSubstitute the values in terms of $d_s$: $25(\\frac{4}{5}d_s) + 20d_s + 18(\\frac{4}{3}d_s) + 12d_s = 1330$
\n$20d_s + 20d_s + 24d_s + 12d_s = 1330$
\n$76d_s = 1330 \\implies d_s = \\frac{1330}{76} = 17.5$
\nNow calculate the amount spent per person for each group:
\n$d_s = 17.5$
\n$w_s = \\frac{4}{5} \\times 17.5 = 14$
\n$t_s = \\frac{4}{3} \\times 17.5 = \\frac{70}{3} \\approx 23.33$
\n$b_s = 17.5$
\nTotal amount spent by each group:
\nWriters: $25 \\times 14 = 350$
\nDoctors: $20 \\times 17.5 = 350$
\nDentists: $18 \\times \\frac{70}{3} = 6 \\times 70 = 420$
\nBank Employees: $12 \\times 17.5 = 210$
\nComparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).
\n<\/section>\n
\nThis problem requires setting up equations based on the given relationships and solving for the per-person cost of one group, then using that to find the costs for others and finally the total expenditure per group.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

25 writers, 20 doctors, 18 dentists and 12 bank employees spent altogether \u20b9 1,330 in a hotel. However, it was found that 5 writers spent as much as 4 doctors, that 12 doctors spent as much as 9 dentists, and that 6 dentists spent as much as 8 bank employees. Out of the four professional … <\/p>\n

Detailed Solution25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge<\/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":[1114,1102],"class_list":["post-92524","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\n25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge<\/title>\n<meta name=\"description\" content=\"The correct answer is B) Dentists. Let $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees. We are given the following relationships: 1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s implies w_s = frac{4}{5}d_s$ 2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s implies 4d_s = 3t_s implies t_s = frac{4}{3}d_s$ 3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s implies 3t_s = 4b_s$ Substitute $t_s$ from (2) into (3): $3(frac{4}{3}d_s) = 4b_s implies 4d_s = 4b_s implies d_s = b_s$ So, we have $w_s = frac{4}{5}d_s$, $t_s = frac{4}{3}d_s$, and $b_s = d_s$. The total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$ Substitute the values in terms of $d_s$: $25(frac{4}{5}d_s) + 20d_s + 18(frac{4}{3}d_s) + 12d_s = 1330$ $20d_s + 20d_s + 24d_s + 12d_s = 1330$ $76d_s = 1330 implies d_s = frac{1330}{76} = 17.5$ Now calculate the amount spent per person for each group: $d_s = 17.5$ $w_s = frac{4}{5} times 17.5 = 14$ $t_s = frac{4}{3} times 17.5 = frac{70}{3} approx 23.33$ $b_s = 17.5$ Total amount spent by each group: Writers: $25 times 14 = 350$ Doctors: $20 times 17.5 = 350$ Dentists: $18 times frac{70}{3} = 6 times 70 = 420$ Bank Employees: $12 times 17.5 = 210$ Comparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).\" \/>\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\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge\" \/>\n<meta property=\"og:description\" content=\"The correct answer is B) Dentists. Let $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees. We are given the following relationships: 1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s implies w_s = frac{4}{5}d_s$ 2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s implies 4d_s = 3t_s implies t_s = frac{4}{3}d_s$ 3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s implies 3t_s = 4b_s$ Substitute $t_s$ from (2) into (3): $3(frac{4}{3}d_s) = 4b_s implies 4d_s = 4b_s implies d_s = b_s$ So, we have $w_s = frac{4}{5}d_s$, $t_s = frac{4}{3}d_s$, and $b_s = d_s$. The total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$ Substitute the values in terms of $d_s$: $25(frac{4}{5}d_s) + 20d_s + 18(frac{4}{3}d_s) + 12d_s = 1330$ $20d_s + 20d_s + 24d_s + 12d_s = 1330$ $76d_s = 1330 implies d_s = frac{1330}{76} = 17.5$ Now calculate the amount spent per person for each group: $d_s = 17.5$ $w_s = frac{4}{5} times 17.5 = 14$ $t_s = frac{4}{3} times 17.5 = frac{70}{3} approx 23.33$ $b_s = 17.5$ Total amount spent by each group: Writers: $25 times 14 = 350$ Doctors: $20 times 17.5 = 350$ Dentists: $18 times frac{70}{3} = 6 times 70 = 420$ Bank Employees: $12 times 17.5 = 210$ Comparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:27:19+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":"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge","description":"The correct answer is B) Dentists. Let $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees. We are given the following relationships: 1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s implies w_s = frac{4}{5}d_s$ 2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s implies 4d_s = 3t_s implies t_s = frac{4}{3}d_s$ 3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s implies 3t_s = 4b_s$ Substitute $t_s$ from (2) into (3): $3(frac{4}{3}d_s) = 4b_s implies 4d_s = 4b_s implies d_s = b_s$ So, we have $w_s = frac{4}{5}d_s$, $t_s = frac{4}{3}d_s$, and $b_s = d_s$. The total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$ Substitute the values in terms of $d_s$: $25(frac{4}{5}d_s) + 20d_s + 18(frac{4}{3}d_s) + 12d_s = 1330$ $20d_s + 20d_s + 24d_s + 12d_s = 1330$ $76d_s = 1330 implies d_s = frac{1330}{76} = 17.5$ Now calculate the amount spent per person for each group: $d_s = 17.5$ $w_s = frac{4}{5} times 17.5 = 14$ $t_s = frac{4}{3} times 17.5 = frac{70}{3} approx 23.33$ $b_s = 17.5$ Total amount spent by each group: Writers: $25 times 14 = 350$ Doctors: $20 times 17.5 = 350$ Dentists: $18 times frac{70}{3} = 6 times 70 = 420$ Bank Employees: $12 times 17.5 = 210$ Comparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).","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\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/","og_locale":"en_US","og_type":"article","og_title":"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge","og_description":"The correct answer is B) Dentists. Let $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees. We are given the following relationships: 1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s implies w_s = frac{4}{5}d_s$ 2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s implies 4d_s = 3t_s implies t_s = frac{4}{3}d_s$ 3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s implies 3t_s = 4b_s$ Substitute $t_s$ from (2) into (3): $3(frac{4}{3}d_s) = 4b_s implies 4d_s = 4b_s implies d_s = b_s$ So, we have $w_s = frac{4}{5}d_s$, $t_s = frac{4}{3}d_s$, and $b_s = d_s$. The total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$ Substitute the values in terms of $d_s$: $25(frac{4}{5}d_s) + 20d_s + 18(frac{4}{3}d_s) + 12d_s = 1330$ $20d_s + 20d_s + 24d_s + 12d_s = 1330$ $76d_s = 1330 implies d_s = frac{1330}{76} = 17.5$ Now calculate the amount spent per person for each group: $d_s = 17.5$ $w_s = frac{4}{5} times 17.5 = 14$ $t_s = frac{4}{3} times 17.5 = frac{70}{3} approx 23.33$ $b_s = 17.5$ Total amount spent by each group: Writers: $25 times 14 = 350$ Doctors: $20 times 17.5 = 350$ Dentists: $18 times frac{70}{3} = 6 times 70 = 420$ Bank Employees: $12 times 17.5 = 210$ Comparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).","og_url":"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:27:19+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\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/","url":"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/","name":"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:27:19+00:00","dateModified":"2025-06-01T11:27:19+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is B) Dentists. Let $w_s, d_s, t_s, b_s$ be the average amount spent by one writer, doctor, dentist, and bank employee, respectively. The number of people in each group is 25 writers, 20 doctors, 18 dentists, and 12 bank employees. We are given the following relationships: 1. 5 writers spend as much as 4 doctors: $5w_s = 4d_s \\implies w_s = \\frac{4}{5}d_s$ 2. 12 doctors spend as much as 9 dentists: $12d_s = 9t_s \\implies 4d_s = 3t_s \\implies t_s = \\frac{4}{3}d_s$ 3. 6 dentists spend as much as 8 bank employees: $6t_s = 8b_s \\implies 3t_s = 4b_s$ Substitute $t_s$ from (2) into (3): $3(\\frac{4}{3}d_s) = 4b_s \\implies 4d_s = 4b_s \\implies d_s = b_s$ So, we have $w_s = \\frac{4}{5}d_s$, $t_s = \\frac{4}{3}d_s$, and $b_s = d_s$. The total amount spent is \u20b9 1330: $25w_s + 20d_s + 18t_s + 12b_s = 1330$ Substitute the values in terms of $d_s$: $25(\\frac{4}{5}d_s) + 20d_s + 18(\\frac{4}{3}d_s) + 12d_s = 1330$ $20d_s + 20d_s + 24d_s + 12d_s = 1330$ $76d_s = 1330 \\implies d_s = \\frac{1330}{76} = 17.5$ Now calculate the amount spent per person for each group: $d_s = 17.5$ $w_s = \\frac{4}{5} \\times 17.5 = 14$ $t_s = \\frac{4}{3} \\times 17.5 = \\frac{70}{3} \\approx 23.33$ $b_s = 17.5$ Total amount spent by each group: Writers: $25 \\times 14 = 350$ Doctors: $20 \\times 17.5 = 350$ Dentists: $18 \\times \\frac{70}{3} = 6 \\times 70 = 420$ Bank Employees: $12 \\times 17.5 = 210$ Comparing the total amounts, the Dentists group spent the maximum amount (\u20b9 420).","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/25-writers-20-doctors-18-dentists-and-12-bank-employees-spent-altoge\/#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":"25 writers, 20 doctors, 18 dentists and 12 bank employees spent altoge"}]},{"@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\/92524","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=92524"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92524\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}