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Before coming to tricks, let\u2019s have a quick recap of the basic concept of ratio and proportion.<\/span><\/b><\/p>\n When we compare two quantities using the method of division, it is known as a ratio. We use the \u2018:\u2019 sign to denote the ratio, represented as p:q.<\/span><\/b><\/p>\n Proportion is a comparison of two ratios. We use \u2018::\u2019 and \u2018=\u2019 signs to denote proportions. If two ratios p:q and r:s have equal value, they are said to be a proportion and represented as p:q::r:s.<\/span><\/b><\/p>\n Now let\u2019s learn about the ratio and proportion tricks.\u00a0<\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> If 2:3 = 8:12\u00a0<\/span><\/p>\n Then, (2 \u00d7 12) = (8 \u00d7 3)<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a024\u00a0 = 24, which satisfies the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> If 2:3 = 8:12\u00a0<\/span><\/p>\n Then, \\frac{2}{8}=\\frac{3}{12}<\/span><\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u21d2 \\frac{1}{4}=\\frac{1}{4}<\/span> , satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example: If 2:3 = 8:12<\/span><\/p>\n Then \\frac{3}{2}=\\frac{12}{8}<\/span><\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 3\/2 = 3\/2, satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n <\/b><\/p>\n \u00a0Example:<\/strong> If 2:3 = 8:12<\/span><\/p>\n Then (2 + 3)\/3 = (8 + 12)\/12<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 \\frac{5}{3}=\\frac{20}{12}<\/span><\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2\\frac{5}{3}=\\frac{5}{3}<\/span> , satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> If 2:3 = 8:12<\/span><\/p>\n Then\\frac{(2-3)}{3}=\\frac{(8-12)}{12}<\/span>\u00a0<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2\\frac{-1}{3}=\\frac{-4}{12}<\/span>\u00a0<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 \\frac{-1}{3}=\\frac{-1}{3}<\/span>, satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> If 2:3 = 8:12<\/span><\/p>\n Then\\frac{(2+3)}{(2-3)}=\\frac{(8+12)}{(8-12)}<\/span> <\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 \\frac{5}{(-1)}=\\frac{20}{-4}<\/span><\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 -5 = -5, satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n Example:<\/strong> If 2:4 = 4:8<\/span><\/p>\n Then 2:8 = \\frac{22}{42}<\/span>2<\/span>2<\/span>\/4<\/span>2<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 \\frac{2}{8}=\\frac{4}{16}<\/span><\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u21d2 \\frac{1}{4}=\\frac{1}{4}<\/span> , satisfying the condition.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n These properties are equally important along with the tricks explained above, So, we must know about these properties to solve problems related to this topic easily and quickly,<\/span><\/p>\n s is fourth proportional to p, q, and r.<\/span><\/p>\n r is the third proportion to p and q.<\/span><\/p>\n The mean proportion between p and q is \u221a(pq)<\/span><\/b><\/span><\/p>\n \u00a0 \\frac{p}{q}>\\frac{r}{s}<\/span>\u00a0<\/span><\/p>\n <\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0p^{2}: 1^{2}<\/span><\/span> is the duplicate ratio,<\/span><\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u221ap:\u221aq is the sub-duplicate ratio, and<\/span><\/p>\n \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0p^{3}: q^{3}<\/span><\/span>\u00a0is the triplicate ratio.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n According to Dividendo rule,\u00a0<\/span><\/p>\n If p:q = r:s, then \\frac{(p+q)} {q} = \\frac{(r+s)} {s}<\/span><\/span><\/b><\/p>\n Here p = 3, q = 4, r = 9, and s = 12.<\/span><\/p>\n We have to verify \\frac{(p+q)}{q}=\\frac{(r+s)}{s}<\/span>.<\/span><\/b><\/p>\n <\/span><\/p>\n Substituting the values of p, q, r, and s.<\/span><\/p>\n \\frac{(3+4)}{4} =\\frac{(9+12)}{12}<\/span><\/span><\/p>\n \u21d2\\frac{7}{4} = \\frac{21}{12}<\/span><\/span><\/p>\n \u21d2\\frac{7}{4} = \\frac{7}{4}<\/span>, which verifies the dividendo rule.<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n We know that the compounded ratio of the ratios (p:q), (r:s), and (t:u) is (prt : qsu).<\/span><\/p>\n So, the compounded ratio of the ratios (2:3), (3:4), and (3:5)<\/span><\/p>\n = (2 \u00d7 3 \u00d7 3):(3 \u00d7 4 \u00d7 5)<\/span><\/p>\n = 18:60<\/span><\/p>\n = 3:10<\/span><\/p>\n <\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” 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link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}” theme_builder_area=”post_content”]<\/p>\n\n
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Some Important Properties of Ratio and Proportion<\/b><\/h2>\n
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<\/span><\/li>\nExamples<\/b><\/h2>\n
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1. If ratios (3:4) and (9:12) are equal in value, verify the Dividendo rule.<\/span><\/b><\/h3>\n
2. Find the compounded ratio of the ratios (2:3), (3:4), and (3:5).<\/span><\/span><\/h3>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n