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.
If $\frac{a}{b}=\frac{c}{d}$, then, show that $\frac{3 a-5 b}{3 a+5 b}=\frac{3 c-5 d}{3 c+5 d}$.
View full solution →If $a, b, c, d$ are in continued proportion, prove that $(b+c)(b+d)=(c+a)(c+d)$.
View full solution →If $\frac{x}{b-c}=\frac{y}{c-a}=\frac{z}{a-b}$, then prove that $a x+b y+c z=0$.
View full solution →If $a: b=c: d$, then prove that $(a+b):(c+d)=\sqrt{a^2+b^2}: \sqrt{c^2+d^2}$.
View full solution →If $b$ is the mean proportion between $a$ and $c$, show that $b(a+c)$ is the mean proportion between $\left(a^2+b^2\right)$ and $\left(b^2+c^2\right)$.
View full solution →Using the properties of proportion, solve for $x$ :
$\frac{\sqrt{6 x}+\sqrt{3 x+7}}{\sqrt{6 x}-\sqrt{3 x+7}}=11.$
View full solution →If $\frac{\sqrt{x+15}+\sqrt{x-6}}{\sqrt{x+15}-\sqrt{x-6}}=\frac{7}{3}$, find the value of $x$
View full solution →If $p=\frac{4 x y}{x+y}$, prove that $\frac{p+2 x}{p-2 x}+\frac{p+2 y}{p-2 y}=2$.
View full solution →If $x=\frac{\sqrt{a+3 b}+\sqrt{a-3 b}}{\sqrt{a+3 b}-\sqrt{a-3 b}}$, prove that $3 b x^2-2 a x+3 b=0$
View full solution →If $a x=b y=c z$, then prove that : $\frac{x^2}{y z}+\frac{y^2}{z x}+\frac{z^2}{x y}=\frac{b c}{a^2}+\frac{c a}{b^2}+\frac{a b}{c^2}$
View full solution →If $\frac{4 a+9 b}{4 c+9 d}=\frac{4 a-9 b}{4 c-9 d}$, then $a: b=$
- A
$c: d$
- B
$d: c$
- C
$c: d+c$
- D
$d: c-d$
View full solution →$x, y, z$ are in continued proportion, then $\frac{x}{z}$ is equal to :
- A
$\frac{y^2}{z^2}$
- B
$\frac{y^2}{x^2}$
- C
$x^2 y^2$
- D
$\frac{x}{y^2}$
View full solution →If three quantities $a, b, c$ are in continued proportion, then the mean proportion between :
- A
$a$ and $c$ is $b$
- B
$b$ and $c$ is a
- C
$c$ and $a$ is $b$
- D
View full solution →Two numbers are in the ratio $1: 4$. If the mean proportion between them is $28$ and third proportional to them is $224$ , then the smaller number is :
View full solution →If $2 x=3 y$ and $4 y=5 z$, then $\frac{8 x}{z}$ is equal to :
View full solution →Assertion (A) : If $\frac{x}{y}=\frac{a}{b}$, then $\frac{x+a}{y+b}=\frac{x-a}{y-b}$
Reason (R) : If $\frac{a}{b}=\frac{c}{d}$, then using componendo and dividendo, we get $\frac{a+b}{a-b}=\frac{c+d}{c-d}$.
View full solution →Assertion (A) : If $\frac{a}{b}=\frac{c}{d}=m$, then $\frac{a+c}{b+d}=m$.
Reason (R) : If for four numbers $a, b, c, d, a: b=c: d$, then $a b=c d$.
View full solution →Assertion (A) : If $a: b:: b: c$, then $b$ is called the mean proportion between $a$ and $c$.
Reason (R) : If $a: b:: b: c$, then $a, b, c$, are said to be in continued proportion.
View full solution →