Question

Find the value of x in the proportion 12 : 15 : : 16 : x​

Answer 1

★ Given :-

The ratio 12 : 15 : : 16 : x

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

★ To Find :-

The value of x in the proportion

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

★ Used Formula :-

$\color{navy}⇢\: \red{ \boxed{ \bf Product \: of \: means = Product \: of \: extremes}} \:$

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

★ Solution :-

The given ratio is 12 : 15 : : 16 : x

The value of x is ?

Here,

$\color{navy} \star\: \red{ \boxed{ \bf Product \: of \: means = Product \: of \: extremes}} \:$

Where,

• 12 & X are the Extremes
• 15 & 16 are the Means

So,

$\: : \: ⟹ \: \bf12 \times x = 15 \times 16$

$\: : \: ⟹ \: \bf12 \times x = 240$

$\: : \: ⟹ \: \bf12 x = 240$

$\displaystyle\: : \: ⟹ \: \bf x = \cancel\frac{240}{12}$

$\red{ \displaystyle\: : \: ⟹ \: \underline{ \boxed{\bf x = 20}}}$

The value of X is 20

Now,

The ratio is 12 : 15 : : 16 : 20

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

Answer 2

Given:

proportion 12 : 15 : : 16 : x​

To Find:

Find the value of x in the proportion

Solution:

When two ratios are equal then it is said that they are in proportion. It is denoted by the '::' sign,  where, on one side 1st ratio is written and on the other side 2nd ratio. If a/b=c/d then we represent it as in proportion form,

a:b::c:d where a,b and c,d are the ratios.

Now in the question, it is given that 12:15::16:x are in proportion and we need to find the value of x, we can express the given proportion as,

$\frac{12}{15} =\frac{16}{x}$

First inversing the equation and then multiplying both sides by 16 we have,

$\frac{15}{12} =\frac{x}{16} \\\frac{15}{12}*16 =\frac{x}{16}*16\\x=\frac{15*16}{12} \\x=20$

Hence, the value of x is 20.