Question

If $ 25,30,x,72 $ are in proportion, then the value of x is?
\[
  A.{\text{ }}30 \\
  B.{\text{ 60}} \\
  C.{\text{ 45}} \\
  D.{\text{ None}} \\
 \]

Answer 1

Hint: Use the property of proportion in order to find some algebraic equation in x. Finally solve the algebraic equation to find the value of unknown variable x.

Complete step-by-step answer:

Given statement: $25,30,x,72$ are in proportion.
As we know that if $a,b,c,d$ are in proportion. Then the relation between them is given by:
$\dfrac{a}{b} = \dfrac{c}{d}$
Comparing the general terms with the given numbers we have:
$
  a = 25 \\
  b = 30 \\
  c = x \\
  d = 72 \\
 $
Now, using the formula above, we have:
$
   \Rightarrow \dfrac{a}{b} = \dfrac{c}{d} \\
   \Rightarrow \dfrac{{25}}{{30}} = \dfrac{x}{{72}} \\
 $
Further solving the equation for the value of x:
$
   \Rightarrow 25 \times 72 = x \times 30 \\
   \Rightarrow x = \dfrac{{25 \times 72}}{{30}} \\
   \Rightarrow x = 60 \\
 $
Hence, the value of x must be 60 so that the given set of numbers are in proportion.
So, the correct option is B.

Note: A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions $\dfrac{a}{b} = \dfrac{c}{d}$ ; or using a colon, \[a:b::c:d{\text{ or }}a:b = c:d\]. Always remember the relation between the proportional numbers.