Tag: composition of ratios
Questions Related to composition of ratios
The reciprocal of $\dfrac {-5}{13}$ is _____
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$\dfrac {5}{13}$
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$\dfrac {-13}{5}$
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$\dfrac {13}{5}$
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$\dfrac {-5}{13}$
The subtriplicate ratio of $a : b$ is ____
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$a^{2} : b^{2}$
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$a^{3} : b^{3}$
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$\sqrt {a} : \sqrt {b}$
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$\sqrt [3]{a} : \sqrt [3]{b}$
The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b} = (a)^{\frac {1}{3}} : (b)^{\frac {1}{3}}$
If $\dfrac {y}{x-z}=\dfrac{y+x}{z}=\dfrac{x}{y}$ then find $x:y:z$
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$1:2:3$
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$3:2:1$
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$4:2:3$
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$2:4:7$
$ \dfrac{y}{x-z}=\dfrac{y+x}{z}=\dfrac{x}{y} $
Now,
$ \dfrac{y}{x-z}=\dfrac{x}{y} $
$ {{y}^{2}}={{x}^{2}}-xz\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......(1) $
And
$ \dfrac{y+x}{z}=\dfrac{x}{y} $
$ {{y}^{2}}+xy=xz\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......(2) $
$ {{x}^{2}}-xz+xy=xz $
$ x-z+y=z $
$ 2z=x+y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......(3) $
$ And $
$ \dfrac{y}{x-z}=\dfrac{y+x}{z} $
$ yz=xy-yz+{{x}^{2}}-xz $
$ 2yz=xy+{{x}^{2}}-xz $
$ 2yz=x\left( y+x \right)-xz $ [From equation (3)]
$ 2yz=2xz-xz $
$ 2yz=xz $
$ 2y=x $
$ \dfrac{x}{y}=\dfrac{2}{1}\,\,\,\,\,\,\,\,......\,\,\left( 4 \right) $
Substituting this value in equation (3), we get
$ 2z=2y+y $
$ 2z=3y $
$ \dfrac{y}{z}=\dfrac{2}{3}\,\,\,\,\,......\,\,\left( 5 \right) $
By equation (4) and (5), we get
$ x:y:z=4:2:3 .$
Hence, this is the answer.
If $\left( {p - q} \right)\,:\left( {q - x} \right)\,$ be the duplicate ratio of $p:q$, then : $\dfrac{1}{p} + \dfrac{1}{q} = \dfrac{1}{x}$
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True
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False
If $2x=3y$ and $4y=5z$, then $x:z=$
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$4:3$
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$8:15$
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$3:4$
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$15:8$
Given,
If $\cfrac{a}{2}=\cfrac{b}{3}=\cfrac{c}{4}$, then $a:b:c=$
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$2:3:4$
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$4:3:2$
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$3:2:4$
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None of these
Given, $\displaystyle \frac{a}{2} = \frac{b}{3} = \frac{c}{4}$
If $a:b=3:4$, then $4a:3b=$
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$4:3$
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$3:4$
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$1:1$
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None of these
Given $a:b=3:4$
What is the compounded ratio of $x : y, y : z$ and $z : w$
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$y : w$
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$x : w$
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$y : z$
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$x : z$
By the defination of compound ratio these ratio can be expressed as
$\dfrac {x}{y} \times \dfrac {y}{z}\times \dfrac {z}{w} = \dfrac {x}{w}$
Hence $x : w$
If $a:b=5:7$ and $b:c=6:11$, then $a:b:c=$
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$35:49:66$
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$30:42:77$
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$30:42:55$
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None of these
$\dfrac{a}{b} = \dfrac{5}{7} $ $\dfrac{b}{c} = \dfrac{6}{11}$
The compounded ratio of (2 : 3), (6 : 11), and (11 : 2) is
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1:2
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2:1
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11:24
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36:121
Required compounded ratio $\displaystyle=\frac{2}{3}\times\frac{6}{11}\times\frac{11}{2}=2:1$