Question

Find the value of $x$ in the given proportion$:$

$2\frac{1}{2}:x::3\frac{1}{2}:4$

Answer 1

• Step $1:$ To find the value of $x$ when the given number are in proportion

As we know that any four numbers $a,b,c$ and $d$ are said to be in proportion if and only if

$a:b::c:d$

$\frac{a}{b}=\frac{c}{d}$

Step $2:$ Given four numbers are in proportion $2\frac{1}{2}:x::3\frac{1}{2}:4$

$\frac{5}{2}:x::\frac{7}{2}:4$

Find the ratio of first and second number and equate it to the ratio of third and fourth number i.e.

$\frac{{\displaystyle \frac{5}{2}}}{{\displaystyle x}}=\frac{{\displaystyle \frac{7}{2}}}{{\displaystyle 4}}$

$\frac{5}{2x}=\frac{7}{8}$

$x=\frac{8\times 5}{2\times 7}$

$x=\frac{4\times 5}{7}$

$x=\frac{20}{7}$

Hence, the value of $x$ is $\frac{20}{7}$ when four numbers $2\frac{1}{2}:x::3\frac{1}{2}:4$ are in proportion.