{"id":212902,"date":"2025-05-08T15:47:54","date_gmt":"2025-05-08T15:47:54","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=212902"},"modified":"2025-05-08T15:47:56","modified_gmt":"2025-05-08T15:47:56","slug":"syafi-has-decided-to-cut-off-15-of-the-length-of-his-hair-today-and-will-continue-tocut-off-15-every-2-months-thereafter","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/08\/syafi-has-decided-to-cut-off-15-of-the-length-of-his-hair-today-and-will-continue-tocut-off-15-every-2-months-thereafter\/","title":{"rendered":"Syafi has decided to cut off 15% of the length of his hair today and will continue tocut off 15% every 2 months thereafter"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Syafi has decided to cut off 15% of the length of his hair today and will continue tocut off 15% every 2 months thereafter. Knowing that his hair is presently 15centimetres long and that it will grow about 8 centimetres in 2 months, how long willhis hair be after his haircut one year from now?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this, we need to model Syafi\u2019s hair length every two months, accounting for <strong>8 cm growth<\/strong> and then a <strong>15% haircut<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-Step Breakdown:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Initial hair length: <strong>15 cm<\/strong><\/li>\n\n\n\n<li>Every 2 months:\n<ul class=\"wp-block-list\">\n<li>Hair grows <strong>8 cm<\/strong><\/li>\n\n\n\n<li>Then, <strong>15% is cut off<\/strong> (i.e., <strong>85% remains<\/strong>)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Let\u2019s go month by month (every 2 months = one cycle). In 1 year, there are <strong>6 cycles<\/strong>:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 1:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 15 cm<\/li>\n\n\n\n<li>Growth: 15 + 8 = <strong>23 cm<\/strong><\/li>\n\n\n\n<li>Cut: 23 \u00d7 0.85 = <strong>19.55 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 2:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 19.55 cm<\/li>\n\n\n\n<li>Growth: 19.55 + 8 = <strong>27.55 cm<\/strong><\/li>\n\n\n\n<li>Cut: 27.55 \u00d7 0.85 = <strong>23.42 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 3:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 23.42 cm<\/li>\n\n\n\n<li>Growth: 23.42 + 8 = <strong>31.42 cm<\/strong><\/li>\n\n\n\n<li>Cut: 31.42 \u00d7 0.85 = <strong>26.71 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 4:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 26.71 cm<\/li>\n\n\n\n<li>Growth: 26.71 + 8 = <strong>34.71 cm<\/strong><\/li>\n\n\n\n<li>Cut: 34.71 \u00d7 0.85 = <strong>29.50 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 5:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 29.50 cm<\/li>\n\n\n\n<li>Growth: 29.50 + 8 = <strong>37.50 cm<\/strong><\/li>\n\n\n\n<li>Cut: 37.50 \u00d7 0.85 = <strong>31.88 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Cycle 6:<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start: 31.88 cm<\/li>\n\n\n\n<li>Growth: 31.88 + 8 = <strong>39.88 cm<\/strong><\/li>\n\n\n\n<li>Cut: 39.88 \u00d7 0.85 = <strong>33.90 cm<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Final Answer: 33.90 cm<\/strong><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300+ words):<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem models a repeated growth and reduction pattern, which is best approached step by step. We are told Syafi cuts off 15% of his hair every 2 months. Between each cut, his hair grows by 8 centimeters. Starting with an initial hair length of 15 cm, we want to determine the length <strong>after one year<\/strong>. One year includes <strong>6 cycles of 2 months<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In each cycle, two things happen sequentially:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Growth:<\/strong> Hair grows by 8 cm.<\/li>\n\n\n\n<li><strong>Haircut:<\/strong> 15% of the new total length is cut off, meaning only 85% of it remains.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Mathematically, we can express each step as:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">New length after each cycle = (Previous length + 8) \u00d7 0.85<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">We apply this operation six times, starting from the original 15 cm. After computing each stage, we find that the hair length keeps increasing, but at a slower rate due to regular cutting. This is a form of <strong>exponential decay with linear growth<\/strong>, a hybrid pattern seen in many real-life scenarios, including finance and biology.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">After completing all six cycles, Syafi\u2019s hair length reaches <strong>approximately 33.90 cm<\/strong>. This result shows that even with regular trimming, the consistent growth of 8 cm every 2 months outweighs the 15% reduction, leading to overall hair length increase. However, the growth rate slightly slows as the absolute amount of hair cut off increases over time.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This type of repeated percentage reduction is common in problems involving depreciation, population models, and exponential change, making it a valuable concept to master.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Syafi has decided to cut off 15% of the length of his hair today and will continue tocut off 15% every 2 months thereafter. Knowing that his hair is presently 15centimetres long and that it will grow about 8 centimetres in 2 months, how long willhis hair be after his haircut one year from now? [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-212902","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212902","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=212902"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/212902\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=212902"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=212902"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=212902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}