{"id":125513,"date":"2023-09-05T19:27:00","date_gmt":"2023-09-05T13:57:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=125513"},"modified":"2023-11-02T10:15:50","modified_gmt":"2023-11-02T04:45:50","slug":"rd-sharma-class-10-solutions-chapter-3-exercise-3-1","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/","title":{"rendered":"RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-125552\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-3-Exercise3.1.jpg\" alt=\"RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-3-Exercise3.1.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Class-10-Solutions-Chapter-3-Exercise3.1-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1:\u00a0<\/strong>The first exercise in this chapter introduces the fundamentals of graphic and algebraic representation of linear equations. The <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-for-maths\/\"><strong>RD Sharma Solutions Class 10<\/strong><\/a> covers key concepts in this and other chapters that are important for students&#8217; exam preparation. The <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-pair-of-linear-equations-in-two-variables\/\"><strong>RD Sharma Solutions for Class 10 Maths Chapter 3<\/strong><\/a> Pair Of Linear Equations In Two Variables Exercise 3.1 PDF is available below for students.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d7a8ad9dd15\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d7a8ad9dd15\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#download-rd-sharma-class-10-solutions-chapter-3-exercise-31-free-pdf\" title=\"Download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 Free PDF\">Download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#access-answers-to-rd-sharma-solutions-class-10-maths-chapter-3-exercise-31-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 10 Maths Chapter 3 Exercise 3.1- Important Question with Answers\">Access answers to RD Sharma Solutions Class 10 Maths Chapter 3 Exercise 3.1- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#faqs-on-rd-sharma-class-10-solutions-chapter-3-exercise-31\" title=\"FAQs on RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1\">FAQs on RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#where-can-i-download-rd-sharma-class-10-solutions-chapter-3-exercise-31-free-pdf\" title=\"Where can I download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 free PDF?\">Where can I download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#is-it-required-to-practice-all-of-the-questions-in-rd-sharma-class-10-solutions-chapter-3-exercise-31\" title=\"Is it required to practice all of the questions in RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?\">Is it required to practice all of the questions in RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/#what-are-the-benefits-of-using-rd-sharma-class-10-solutions-chapter-3-exercise-31\" title=\"What are the benefits of using RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?\">What are the benefits of using RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-10-solutions-chapter-3-exercise-31-free-pdf\"><\/span>Download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-3-Exercise-3.1.pdf\">RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solution-Class-10-Chapter-3-Exercise-3.1.pdf\", \"#example1\");<\/script><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-10-maths-chapter-3-exercise-31-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 10 Maths Chapter 3 Exercise 3.1- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1<\/strong>.\u00a0<strong>Akhila went to a fair in her village. She wanted to enjoy rides on the Giant Wheel and play Hoopla (a game in which you throw a rig on the items in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla is half the number of rides she had on the giant wheel. Each ride costs\u00a0<\/strong>\u20b9<strong>3 and a game of hoopla costs\u00a0<\/strong>\u20b9<strong>4. If she spent\u00a0<\/strong>\u20b9<strong>20 in the fair, represent this situation algebraically and graphically.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>Let \u2018x\u2019 be the number of rides Akhila had on the giant wheel.<\/strong><\/p>\n<p><strong>And, let \u2018y\u2019 be the number of times she played Hoopla.<\/strong><\/p>\n<p><strong>From the question, we can write the below pair of equations.<\/strong><\/p>\n<p><strong>y = (1\/2)x\u00a0<\/strong>\u21d2 x -2y = 0\u2026\u2026. (i)<\/p>\n<p>3x + 4y = 20\u2026\u2026. (ii)<\/p>\n<p>To represent these equations graphically, we need at least two solutions for each (i) and (ii).<\/p>\n<p>And let\u2019s put them in a table for each:<\/p>\n<p>For equation (i),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td><strong>y = (1\/2)x<\/strong><\/td>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For equation (ii),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>0<\/td>\n<td>20\/3<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>y = (20 \u2013 3x)\/4<\/td>\n<td>5<\/td>\n<td>0<\/td>\n<td>2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When:<\/p>\n<p>The solution of the variable is zero; the equation can be solved easily. Putting x =0 in equation (ii), we get<\/p>\n<p>4y = 20 \u21d2y = 5<\/p>\n<p>Similarly putting y = 0 in equation (ii) we get<\/p>\n<p>3x = 20 \u21d2x = 20\/3\u00a0but it is not an integer so it is not easy to plot on graph paper.<\/p>\n<p>So, we chose y=2, which gives x =4 as an integer value.<\/p>\n<p>The above can be plotted in a graph as below:<\/p>\n<p><img class=\"\" title=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 1\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/10\/r-d-sharma-solutions-for-class-10-maths-chapter-3.png\" alt=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 1\" width=\"512\" height=\"239\" \/><\/p>\n<p>We can observe that the two lines represent the equations (i) and (ii) intersect at a single point.<\/p>\n<p><strong>2.<\/strong>\u00a0<strong>Aftab tells his daughter, \u201cSeven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.\u201d Is not this interesting? Represent this situation algebraically and graphically.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Let the present age of Aftab and his daughter be x and y, respectively.<\/p>\n<p>Hence, seven years ago,<\/p>\n<p>Age of Aftab = x \u2013 7 and Age of his daughter = y \u2013 7<\/p>\n<p>According to the given condition,<\/p>\n<p>x \u2013 7 = 7 (y \u2013 7) \u21d2 x \u2013 7y = -42\u2026\u2026\u2026 (i)<\/p>\n<p>Three years from the present age,<\/p>\n<p>x + 3 = 3 (y + 3) \u21d2x \u2013 3y = 6\u2026\u2026\u2026..(ii)<\/p>\n<p>Therefore, equations (i) and (ii) represent the situation algebraically.<\/p>\n<p>To represent these equations graphically, we need at least two solutions for each (i) and (ii).<\/p>\n<p>And let\u2019s put them in a table for each:<\/p>\n<p>For equation (i),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>-7<\/td>\n<td>0<\/td>\n<td>7<\/td>\n<\/tr>\n<tr>\n<td>y = (x + 42)\/7<\/td>\n<td>5<\/td>\n<td>6<\/td>\n<td>7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For equation (ii),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>6<\/td>\n<td>3<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>y = (x \u2013 6)\/3<\/td>\n<td>0<\/td>\n<td>-1<\/td>\n<td>-2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The above can be plotted in a graph as below:<\/p>\n<p><img class=\"\" title=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 2\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/10\/r-d-sharma-solutions-for-class-10-maths-chapter-3-1.png\" alt=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 2\" width=\"559\" height=\"276\" \/><\/p>\n<p><strong>3.<\/strong>\u00a0<strong>The path of train A is given by the equation 3x+4y-12 =0 and the path of another train B is given by the equation 6x+8y-48 =0. Represent this situation graphically.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given a pair of linear equations that represents the paths of train A and train B,<\/p>\n<p>3x + 4y \u2013 12 = 0\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.. (i)<\/p>\n<p>6x + 8y \u2013 48 = 0 \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.. (ii)<\/p>\n<p>To represent these equations graphically, we need at least two solutions for each (i) and (ii).<\/p>\n<p>And let\u2019s put them in a table for each:<\/p>\n<p>For equation (i),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>0<\/td>\n<td>4<\/td>\n<\/tr>\n<tr>\n<td>y = (12 \u2013 3x)\/4<\/td>\n<td>3<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For equation (i),<\/p>\n<table class=\"table table-bordered\">\n<tbody>\n<tr>\n<td>x<\/td>\n<td>0<\/td>\n<td>8<\/td>\n<\/tr>\n<tr>\n<td>y = (48 \u2013 6x)\/8<\/td>\n<td>6<\/td>\n<td>0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The above can be plotted in a graph as below:<\/p>\n<p><img class=\"\" title=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 3\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2019\/10\/r-d-sharma-solutions-for-class-10-maths-chapter-3-2.png\" alt=\"R D Sharma Solutions For Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables ex 3.1 - 3\" width=\"540\" height=\"252\" \/><\/p>\n<p>We have provided complete details of RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 10, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-class-10-solutions-chapter-3-exercise-31\"><\/span>FAQs on RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1631107836977\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-class-10-solutions-chapter-3-exercise-31-free-pdf\"><\/span>Where can I download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631108044790\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-it-required-to-practice-all-of-the-questions-in-rd-sharma-class-10-solutions-chapter-3-exercise-31\"><\/span>Is it required to practice all of the questions in RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, all of the questions in RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 must be learned. These questions may appear on both board exams and class tests. Students will be prepared for their board exams if they learn these questions.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1631108594056\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-benefits-of-using-rd-sharma-class-10-solutions-chapter-3-exercise-31\"><\/span>What are the benefits of using RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>1. Correct answers according to the last CBSE guidelines and syllabus.<br \/>2. The RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 is written in simple language to assist students in their board examination, &amp; competitive examination preparation.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1:\u00a0The first exercise in this chapter introduces the fundamentals of graphic and algebraic representation of linear equations. The RD Sharma Solutions Class 10 covers key concepts in this and other chapters that are important for students&#8217; exam preparation. The RD Sharma Solutions for Class 10 Maths Chapter &#8230; <a title=\"RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-class-10-solutions-chapter-3-exercise-3-1\/\" aria-label=\"More on RD Sharma Class 10 Solutions Chapter 3 Exercise 3.1 (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":125552,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3243,9206,73520,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125513"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=125513"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125513\/revisions"}],"predecessor-version":[{"id":501119,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/125513\/revisions\/501119"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/125552"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=125513"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=125513"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=125513"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}