Question

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

$\frac{1}{15}:\frac{1}{4}::x:\frac{1}{5}$

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 $\frac{1}{15}:\frac{1}{4}::x:\frac{1}{5}$

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

$\frac{{\displaystyle \frac{1}{15}}}{{\displaystyle \frac{1}{4}}}=\frac{x}{{\displaystyle \frac{1}{5}}}$

$\frac{4}{15}=5x$

$x=\frac{4}{15\times 5}$

$x=\frac{4}{75}$

Hence, the value of $x$ is $\frac{4}{75}$ when four numbers $\frac{1}{15}:\frac{1}{4}::x:\frac{1}{5}$ are in proportion.