{"id":5457,"date":"2021-12-08T14:39:53","date_gmt":"2021-12-08T14:39:53","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=5457"},"modified":"2022-01-03T07:15:54","modified_gmt":"2022-01-03T07:15:54","slug":"unitary-method-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/unitary-method-with-examples-and-faqs\/","title":{"rendered":"Unitary Method with Examples and FAQs"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Unitary Method with Examples and FAQs<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>What is the unitary method?<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The unitary method is a method of calculating the value of a single unit from a given value. It can further be used to calculate the value of the required number of units. This is the basic and most commonly used method for calculation in many math problems.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example,<\/span><\/p>\n<p>The cost of a dozen of bananas is <span style=\"font-weight: 400;\">\u20b9<\/span>36. what will be the cost of 7 bananas?<\/p>\n<p>Solving by unitary method:<\/p>\n<p>Given cost of a dozen of bananas is <span style=\"font-weight: 400;\">\u20b9<\/span>36<\/p>\n<p>Then cost of 1 banana <span class=\"katex-eq\" data-katex-display=\"false\">=\\frac{\\text { Total cost of bananas }}{\\text { Total number of bananas }}=\\frac{36}{12}=\u20b9 3<\/span><\/p>\n<p>Therefore the cost of 1 banana <span class=\"katex-eq\" data-katex-display=\"false\">\\times 7=\u20b9 3 \\times 7=\u20b9 21<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>Unitary Method in Ratio and Proportion<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><span style=\"font-weight: 400;\">This method is commonly used to find ratios between two given quantities.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example:<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A and B are employees of a company. A\u2019s salary per annum is \u20b92,40,000 and that of B is \u20b922000 per month. A saves \u20b95000 a month a B saves \u20b912000 a month. What is the ratio of their monthly expenditure?<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A\u2019s salary is \u20b92,40,000 per annum, i.e., for 12 months.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234 <\/span><span style=\"font-weight: 400;\">A\u2019s monthly salary\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">=\\frac{\\text { Total salary }}{\\text { Number of months }}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">=\\frac{240000}{12}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">=20000<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, A earns \u20b920,000 per month.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A\u2019s monthly income is \u20b920,000 and savings is \u20b95,000.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234 <\/span><span style=\"font-weight: 400;\">A\u2019s monthly expenditure = Monthly income \u2013 Monthly savings\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = \u20b920,000 &#8211; \u20b95,000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = \u20b915,000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">B\u2019s monthly income is \u20b922,000 and savings is \u20b912,000.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234 <\/span><span style=\"font-weight: 400;\">B\u2019s monthly expenditure = Monthly income \u2013 Monthly savings\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = \u20b922,000 &#8211; \u20b912,000<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 = \u20b910,000<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><br \/>\u2234 The ratio of their monthly expenditure is given by,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\frac{A^{\\prime} s \\text { monthly expenditure }}{B^{\\prime} s \\text { monthly expenditure }}=\\frac{15,000}{10,000}=\\frac{3}{2}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Types of Unitary Method<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><span style=\"font-weight: 400;\">The calculations involved in the unitary method can have two variations, which are:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h3><b>(1) Direct Variation<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">In the case of direct variation if one quantity increases the other quantity will also increase.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, if the number of items purchased is increased then in that case the cost will also increase. Here, the number of items purchased and the cost of items are in a relationship with one another directly, i.e., if one increases the other will also increase.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h3><b>(2) Indirect Variation<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">In the case of indirect variation if one quantity increases the other quantity will decrease.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example, suppose a car is moving at a given speed to reach a fixed distance. Suddenly if the speed of the car is increased then the distance can be reached in a lesser span of time. Here, the speed of the car and the travelling time are in a relationship with one another indirectly, i.e., if one increases the other will decrease.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Applications of Unitary Method<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><span style=\"font-weight: 400;\">The unitary method can be used to solve a lot of mathematics problems in day-to-day life. Some of the ways in which the method is used are:<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It can be used in evaluating the price of an item when the price of a number of items is given.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It can be used to solve business problems by calculating profit and loss.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It is even used in calculating the percentage of a quantity.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">It finds use in calculating the amount of work and time taken to complete the work.<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>Examples<\/b><\/h2>\n<p><b><\/b><\/p>\n<p><strong>Example 1<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> A car is travelling at a speed of 120 kmph. What is the distance covered in 2 hours?<\/span><\/p>\n<p><strong>Solution:\u00a0<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">We know,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Distance = Speed \u00d7 Time<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Given: Speed = 120 kmph<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u21d2 The distance travelled by car in an hour is 120 km.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234 the distance covered by car in 2 hours <\/span><span style=\"font-weight: 400;\">= distance covered by a car in an hour \u00d7 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u21d2 Required distance covered = 120 \u00d7 2 = 240 km<\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the car covered a distance of 240 km in 2 hours.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><strong>Example 2<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> Anushka goes to a stationery shop to buy some pencils. The shopkeeper informs her that the cost of 5 pencils is \u20b915. Calculate the cost of 20 pencils by the unitary method.<\/span><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">It is given that the cost of 5 pencils is \u20b915.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow \\text { cost of } 1 \\text { pencil }=\\frac{\\text { Total cost of pencils }}{\\text { Total number of pencils }}=\\frac{15}{5}=\u20b9 3<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Now, we will calculate the cost of 20 pencils.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cost of 20 pencils = Cost of 1 pencil \u00d7 Number of pencils = 3 \u00d7 20 = \u20b960<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the cost of 20 pencils is \u20b960.<\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; 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width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Frequently Asked Questions<span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h1>\n<ol><\/ol>\n<h3><strong>Q1: What is the unitary method?<br \/><\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: <\/strong>The unitary method is a method with the help of which the value of a single unit can be calculated and further with the help of this value we can find the values of the required number of units.<br \/><\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<h3><strong>Q2. What are the types of unitary methods?<\/strong><\/h3>\n<p><strong>Ans: <\/strong>There are two types of the unitary method (1) Direct variation and (2) Inverse variation.<br \/><strong><\/strong><\/p>\n<h3><strong>Q3. How to Solve Unitary Method Questions?<\/strong><\/h3>\n<p><strong>Ans: <\/strong><span style=\"font-weight: 400;\">To solve questions based on the unitary method, at first, find the number of objects at the unit level, then find it for higher values.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">For example:\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">If the cost of 12 candies is \u20b924, then to find the cost of 8 candies, it is better to first find the cost of 1 candy.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It is given that the cost of 12 candies is \u20b924.<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\Rightarrow \\text { cost of } 1 \\text { candy }=\\frac{\\text { Total cost of candies }}{\\text { Total number of candies }}=\\frac{24}{12}=\u20b9 2<\/span>\n<p><span style=\"font-weight: 400;\">Then we multiply it by 8 to get the cost of 8 candies.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Cost of 8 candies = Cost of 1 candy \u00d7 Number of candies = 2 \u00d7 8 = \u20b916<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the cost of 8 candies is \u20b916.<\/span><strong><\/strong><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta Description: We can calculate the sum of the terms in a geometric progression using the formula  S = a(1-r^n)\/(1-r) when r < 1 and  S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - 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