Question

The third proportion to 0.36 and 0.48 is
A.0.64
B.0.1728
C.0.42
D.0.94

Answer 1

Hint: Three proportional numbers are generally represented as \[a:b::b:c\] , where \[a\] is the first term, \[b\] is the second term and \[c\] is the third term.
In this question two numbers are given where 0.36 is the first proportional term and 0.48 is the second proportional term, so by using the third proportional formula we will find the third proportion to 0.36 and 0.48.
In the third proportion: represents fraction sign and:: represents the equals to sign.
 \[\left( : \right) \Rightarrow \left( / \right)\]
 \[\left( {::} \right) \Rightarrow \left( = \right)\]

Complete step-by-step answer:
Given the numbers whose third proportion is to be find are 0.36 and 0.48
Let the third proportion to 0.36 and 0.48 be \[x\]
Now we know that the three proportional numbers are generally represented as \[a:b::b:c\] and the first two numbers are given as
 \[
  a = 0.36 \\
  b = 0.48 \;
 \]
Now we substitute the given numbers in the third proportion formula to find the third proportion as
 \[
  a:b::b:c \\
   \Rightarrow 0.36:0.48 = 0.48:x \;
 \]
By solving this we get
 \[
  \dfrac{{0.36}}{{0.48}} = \dfrac{{0.48}}{x} \\
   \Rightarrow x = \dfrac{{0.48 \times 0.48}}{{0.36}} \\
   \Rightarrow x = 0.64 \;
 \]
Hence we get \[x = 0.64\]
Therefore we can say the third proportion to 0.36 and 0.48 is 0.64
 \[
  a:b::b:c \\
   \Rightarrow 0.36:0.48 = 0.48:0.64 \\
 \]
So, the correct answer is “0.64”.

Note: Another method to solve this question is in proportional numbers the product of extremes is equal to the product of the means. Such that in \[a:b::b:c\]
 \[b \times b = a \times c\]
In this question we are given the first two terms which are represented as \[0.36:0.48 = 0.48:x\] and since the product of extremes is equal to the product of the mean, hence we can write
 \[0.48 \times 0.48 = x \times 0.36\]
This is equal
 \[
  x = \dfrac{{0.48 \times 0.48}}{{0.36}} \\
   = 0.64 \;
 \]
Hence this method also gives the third term as \[0.64\] .