Algebraic Ratio and Proportion

The ratio of two quantities $p$ and $q$ of the same unit is written as—

In the ratio $p:q$, the quantity $p$ is called the—

In the ratio $p:q$, the quantity $q$ is called the—

For a ratio $p:q$ to be valid, the two quantities must be of—

A ratio is expressed without unit because—

Express $3.5:5.6$ in the form $1:a$. The value of $a$ is—

Express $3.5:5.6$ in the form $b:1$. The value of $b$ is—

If $x:y = 5:6$, then $3x:5y$ in simplest form is—

The number of cars at $10$ A.M. is two times the number at $8$ A.M. The ratio of cars at $10$ A.M. to that at $8$ A.M. is—

The ratio of $200$ g and $1$ kg is—

Which is true for any ratio $a:b$ where $a, b > 0$?

The ratio $0.4 : 0.5$ in simplest form is—

If four quantities $a,b,c,d$ form a proportion, the relationship is—

If $a:b = c:d$, then which is true?

In proportion $a:b = c:d$, the four quantities—

If two triangles have bases $a$ and $b$ and the same height $h$, the ratio of their areas $A:B$ equals—

In proportion $a:b = c:d$, the product of extremes equals the product of—

If $3:4 = 6:x$, then $x =$

If $a:5 = 8:10$, then $a =$

If $9:x = x:25$, then $x =$

The fourth proportional of $3, 4, 9$ is—

The fourth proportional of $5, 7, 25$ is—

If $a:b = b:c$, then $a, b, c$ are said to be—

If $a, b, c$ are in continued proportion, then—

In continued proportion $a:b = b:c$, the term $b$ is the—

In continued proportion $a:b = b:c$, the term $c$ is the—

The mid-proportional of $4$ and $9$ is—

The mid-proportional of $3$ and $12$ is—

The third proportional of $4$ and $6$ is—

The third proportional of $9$ and $12$ is—

If $b, a, c$ are in continued proportion, then—

In continued proportion all the quantities must be—

If $a, b, c$ are in continued proportion, then $\dfrac{a}{c}$ equals—

If $a, b, c$ are continued proportional and $a=2$, $b=6$, then $c =$

If $a, b, c$ are continued proportional and $b=4$, $c=8$, then $a =$

If $a, b, c, d$ are continued proportional, then $\dfrac{a}{d}$ equals—

The value of $b$ if $5, b, 20$ are continued proportional is—

If $a, b, c$ are continued proportional, $b$ is the—

By invertendo, if $a:b = c:d$, then—

By alternendo, if $a:b = c:d$, then—

If $2:3 = 4:6$, by invertendo we get—

If $2:3 = 4:6$, by alternendo we get—

The proof of invertendo from $\dfrac{a}{b} = \dfrac{c}{d}$ uses the step—

The proof of alternendo uses the step—

If $\dfrac{x}{2} = \dfrac{y}{3}$, by alternendo we get—

If $\dfrac{a}{b} = \dfrac{c}{d}$, by invertendo we get—

From $a:b = c:d$, by combining alternendo and invertendo we obtain—

If $\dfrac{p}{q} = \dfrac{r}{s}$, then by alternendo $\dfrac{p}{r} =$

Componendo: if $a:b = c:d$, then—

Dividendo: if $a:b = c:d$, then—

Componendo-Dividendo: if $a:b = c:d$, then—

Componendo is proved by—

Dividendo is proved by—

Componendo-Dividendo is obtained by—

Apply componendo on $\dfrac{3}{2} = \dfrac{6}{4}$ to get—

Apply dividendo on $\dfrac{5}{3} = \dfrac{10}{6}$ to get—

Apply componendo-dividendo on $\dfrac{a}{b} = \dfrac{c}{d}$ to get—

From $\dfrac{a}{b} = \dfrac{c}{d}$, the value of $\dfrac{a^2+b^2}{a^2-b^2}$ is—

If $\dfrac{a}{b} = \dfrac{c}{d}$, then $\dfrac{a^2+b^2}{a^2-b^2}$ also equals—

If $\dfrac{a+b}{a-b} = \dfrac{5}{3}$, then $\dfrac{a}{b} =$

If $\dfrac{x+1}{x-1} = \dfrac{3}{2}$, then $x =$

From $\dfrac{a^2+b^2}{a^2-b^2} = \dfrac{ac+bd}{ac-bd}$, the underlying given is—

If $a, b, c$ are continued proportional, then $\left(\dfrac{a+b}{b+c}\right)^2$ equals—

If $a:b = b:c$, then $\dfrac{a^2 + b^2}{b^2 + c^2}$ equals—

If $a:b = b:c$, then $\dfrac{a+b}{b+c}$ equals—

If $\dfrac{a}{b} = \dfrac{c}{d} = \dfrac{e}{f} = \dfrac{g}{h} = k$, then $\dfrac{a+c+e+g}{b+d+f+h} =$

If $\dfrac{a}{b} = \dfrac{c}{d} = \dfrac{e}{f}$, then $\dfrac{a+c+e}{b+d+f}$ equals—

The proof of the sum rule sets each ratio equal to $k$ and uses—

If $\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{5}$, then $\dfrac{x+y+z}{2+3+5}$ equals—

If $\dfrac{a}{b+c} = \dfrac{b}{c+a} = \dfrac{c}{a+b}$ and $a+b+c \ne 0$, then by the sum rule each ratio equals—

The sum rule equality $\dfrac{a+c+e+g}{b+d+f+h} = k$ requires—

If $\dfrac{2}{3} = \dfrac{4}{6} = \dfrac{6}{9}$, then $\dfrac{2+4+6}{3+6+9}$ equals—

Two persons $A$ and $B$ traverse a fixed distance in $t_1$ and $t_2$ minutes respectively. The ratio $v_1 : v_2$ of their average velocities is—

If two cars cover the same distance in $5$ and $4$ minutes, the ratio of their speeds is—

The ratio of present ages of father and son is $7:2$, and after $5$ years it becomes $8:3$. Father's present age is—

In the same problem (father:son $7:2$ becomes $8:3$ after $5$ years), the son's present age is—

Sum of ages of father and son is $70$ years. $7$ years ago the ratio of their ages was $5:2$. Father's present age is—

In the same problem, the ratio of their ages after $5$ years from now is—

A man of height $r$ stands at distance $p$ metres from a light-post and casts a shadow of length $s$. The height of the light-post is—

The ratio of two numbers is $3:4$ and their L.C.M. is $180$. The numbers are—

A thing is bought and then sold at $28\%$ loss. Ratio of buying cost to selling cost is—

The ratio of absent and present students of a day in a class is $1:4$. Percentage of absent students with respect to total is—

If $a:b = c:d$, then $\dfrac{ac+bd}{ac-bd}$ equals—

The proof of $\dfrac{a^2+b^2}{a^2-b^2} = \dfrac{ac+bd}{ac-bd}$ given $\dfrac{a}{b} = \dfrac{c}{d}$ uses the substitution—

If $\dfrac{a^3+b^3}{a-b+c} = a(a+b)$, then—

The proof of $\left(\dfrac{a+b}{b+c}\right)^2 = \dfrac{a^2+b^2}{b^2+c^2}$ given $a:b = b:c$ uses the substitution $b^2 = ac$ and the expansion—

If $\dfrac{a+b}{b+c} = \dfrac{c+d}{d+a}$, then—