Sample QuestionsRatio and Proportion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the compounded ratio of the following:
15: 16 and 8 : 5
Find the ratio of the following in the simplest fcrm:
Rs 5.40 and 180 paise
Find the ratio of the following in the simplest fcrm:
$432$ and $120$
View full solution →Find the ratio of the following in the simplest fcrm:
$5.60$ and $2.40$
View full solution →If $a: b:: c: d:: e: f$, then prove that $\frac{a e+b f}{a e-b f}=\frac{c e+d f}{c e-d f}$
View full solution →If $\frac{1}{12}, x$ and $\frac{1}{75}$ are in continued proportion, find $x$.
View full solution →Find the value of the unknown in the following proportion :
$3 : 4 : : p : 12$
View full solution →Find the value of the unknown in the following proportion :
$5 : 12 :: 15 : x$
View full solution →Find the duplicate ratio of the following:
$\frac{2}{3}: \frac{4}{9}$
View full solution →If $p, q$ and $r$ in continued proportion, then prove the following :
$p ^2- q ^2+ r ^2= q ^4\left(\frac{1}{ p ^2}-\frac{1}{ q ^2}-\frac{1}{ r ^2}\right)$
View full solution →If p, q and r in continued proportion, then prove the following:
$(p + q + r )(p - q + r) = p^2 + q^2 + r^2$
View full solution →If $p, q$ and $r$ in continued proportion, then prove the following:
$(p^2 - q^2)(q^2 + r^2) = (q^2 - r^2)(p^2 + q^2)$
View full solution →If $(7m +8n)(7p - 8q) = (7m - 8n)(7p + 8q),$ then prove that $m: n = p: q$
View full solution →If $a: b:: c: d$, then prove that
$\frac{4 a+9 b}{4 c+9 d}=\frac{4 a-9 b}{4 c-9 d}$
View full solution →If $a: b=c: d$, then prove that $\frac{a^2+c^2}{b^2+d^2}=\frac{a c}{b c}$
View full solution →If $x =\frac{ pab }{ a + b }$, then prove that $\frac{ x + pa }{ x - pa }+\frac{ x + pb }{ x - pb }=\frac{2\left( a ^2- b ^2\right)}{ ab }$
View full solution →If $x=\frac{\sqrt[3]{m+1}+\sqrt[3]{m-1}}{\sqrt[3]{m+1}+\sqrt[3]{m-1}}$ then prove that $x^3-3 m x^2+3 x=m$
View full solution →If $a, b, c$ and dare in continued proportion, then prove that
$(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)^2 $
View full solution →If $a, b, c$ and dare in continued proportion, then prove that
$\sqrt{(a+b+c)(b+c+d)}=\sqrt{a b}+\sqrt{b c}+\sqrt{c d}$
View full solution →If $u, v, w$, and $x$ are in continued proportion, then prove that $(2 u+3 x):(3 u+4 x)::\left(2 u^3+3 v^3\right):$
$\left(3 u ^3+4 v ^3\right)$
$( pqr )^2\left(\frac{1}{ p ^4}+\frac{1}{ q ^4}+\frac{1}{ r ^4}\right)=\frac{ p ^4+ q ^4+ r ^4}{ q ^2}$
View full solution →If $u, v, w$, and $x$ are in continued proportion, then prove that $(2 u+3 x):(3 u+4 x)::\left(2 u^3+3 v^3\right):\left(3 u^3+4 v^3\right)$
View full solution →If $p, q, r$ ands are In continued proportion, then prove that $(p^3+q^3+r^3) ( q^3+r^3+s^3) : : P : s$
View full solution →If $a: b=c: d$, then prove that $\frac{a^2+a b+b^2}{a^2-a b+b^2}=\frac{c^2+c d+d^2}{c^2-c d+d^2}$
View full solution →If $\frac{7 a +12 b }{7 c +12 d }$ then prove that $\frac{ a }{ b }=\frac{ c }{ d }$
View full solution →