{"id":90616,"date":"2025-06-01T10:32:12","date_gmt":"2025-06-01T10:32:12","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90616"},"modified":"2025-06-01T10:32:12","modified_gmt":"2025-06-01T10:32:12","slug":"a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/","title":{"rendered":"A tree is at present 9 feet tall. If every year it grows 1\/9 th of its"},"content":{"rendered":"

A tree is at present 9 feet tall. If every year it grows 1\/9 th of its height, what will be the height of the tree after three years?<\/p>\n

[amp_mcq option1=”12 feet” option2=”12.34 feet” option3=”13 feet” option4=”13.10 feet” correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2021<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nIf a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet.
\n<\/section>\n
\n– The current height of the tree is H\u2080 = 9 feet.
\n– The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern.
\n– After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9).
\n– After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2.
\n– After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3.
\n– Substitute the initial height H\u2080 = 9 feet:
\n– H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729).
\n– H\u2083 = 9000 \/ 729.
\n– Simplify the fraction by dividing numerator and denominator by 9:
\n– H\u2083 = 1000 \/ 81.
\n– Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567…
\n– Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.
\n<\/section>\n
\nThe alternative interpretation, where the tree grows 1\/9th of the *original* height (1 foot) each year, would result in a height of 9 + 3*1 = 12 feet after 3 years. Since 12.34 is an option and 12 is also an option, the wording “1\/9 th of its height” generally implies growth relative to the current height unless otherwise specified, leading to the compounding calculation.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

A tree is at present 9 feet tall. If every year it grows 1\/9 th of its height, what will be the height of the tree after three years? [amp_mcq option1=”12 feet” option2=”12.34 feet” option3=”13 feet” option4=”13.10 feet” correct=”option2″] This question was previously asked in UPSC CAPF – 2021 Download PDFAttempt Online If a tree … <\/p>\n

Detailed SolutionA tree is at present 9 feet tall. If every year it grows 1\/9 th of its<\/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":[1110,1102],"class_list":["post-90616","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1110","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nA tree is at present 9 feet tall. If every year it grows 1\/9 th of its<\/title>\n<meta name=\"description\" content=\"If a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet. - The current height of the tree is H\u2080 = 9 feet. - The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern. - After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9). - After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2. - After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3. - Substitute the initial height H\u2080 = 9 feet: - H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729). - H\u2083 = 9000 \/ 729. - Simplify the fraction by dividing numerator and denominator by 9: - H\u2083 = 1000 \/ 81. - Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567... - Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.\" \/>\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-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A tree is at present 9 feet tall. If every year it grows 1\/9 th of its\" \/>\n<meta property=\"og:description\" content=\"If a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet. - The current height of the tree is H\u2080 = 9 feet. - The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern. - After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9). - After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2. - After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3. - Substitute the initial height H\u2080 = 9 feet: - H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729). - H\u2083 = 9000 \/ 729. - Simplify the fraction by dividing numerator and denominator by 9: - H\u2083 = 1000 \/ 81. - Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567... - Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:32:12+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 tree is at present 9 feet tall. If every year it grows 1\/9 th of its","description":"If a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet. - The current height of the tree is H\u2080 = 9 feet. - The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern. - After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9). - After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2. - After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3. - Substitute the initial height H\u2080 = 9 feet: - H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729). - H\u2083 = 9000 \/ 729. - Simplify the fraction by dividing numerator and denominator by 9: - H\u2083 = 1000 \/ 81. - Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567... - Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.","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-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/","og_locale":"en_US","og_type":"article","og_title":"A tree is at present 9 feet tall. If every year it grows 1\/9 th of its","og_description":"If a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet. - The current height of the tree is H\u2080 = 9 feet. - The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern. - After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9). - After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2. - After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3. - Substitute the initial height H\u2080 = 9 feet: - H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729). - H\u2083 = 9000 \/ 729. - Simplify the fraction by dividing numerator and denominator by 9: - H\u2083 = 1000 \/ 81. - Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567... - Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:32:12+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-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/","url":"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/","name":"A tree is at present 9 feet tall. If every year it grows 1\/9 th of its","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:32:12+00:00","dateModified":"2025-06-01T10:32:12+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"If a tree is 9 feet tall and grows 1\/9th of its height every year, its height after three years will be approximately 12.34 feet. - The current height of the tree is H\u2080 = 9 feet. - The growth each year is 1\/9th of the height at the beginning of that year. This is a compound growth pattern. - After 1 year, height H\u2081 = H\u2080 + (1\/9)H\u2080 = H\u2080(1 + 1\/9) = H\u2080(10\/9). - After 2 years, height H\u2082 = H\u2081 + (1\/9)H\u2081 = H\u2081(1 + 1\/9) = H\u2081(10\/9) = H\u2080(10\/9)(10\/9) = H\u2080(10\/9)\u00b2. - After 3 years, height H\u2083 = H\u2082 + (1\/9)H\u2082 = H\u2082(1 + 1\/9) = H\u2082(10\/9) = H\u2080(10\/9)\u00b3. - Substitute the initial height H\u2080 = 9 feet: - H\u2083 = 9 * (10\/9)\u00b3 = 9 * (1000 \/ 729). - H\u2083 = 9000 \/ 729. - Simplify the fraction by dividing numerator and denominator by 9: - H\u2083 = 1000 \/ 81. - Calculate the decimal value: 1000 \u00f7 81 \u2248 12.34567... - Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/a-tree-is-at-present-9-feet-tall-if-every-year-it-grows-1-9-th-of-its\/#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 tree is at present 9 feet tall. 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