Question

Find the 4th proportional to 4, 16 and 7 ?
A) 28
B) 29
C) 22
D) 25

Answer 1

Hint: Here the given question based on the concept of Proportion, we have to find the 4th proportional of given number. Solving proportional equations is fairly trivial, we know the basic equation transformation laws - multiplying and dividing both sides by the same number is all that is required.

Complete step-by-step solution:
When two ratios are equal, the four quantities composing them are said to be proportional.
Hence, \[\dfrac{p}{q} = \dfrac{r}{s}\] or, \[p:q = r:s\], then p, q, r, s are in proportional and is written as \[p:q::r:s\],
where symbol '::' represents proportion and it is read as 'p is to q' as 'r is to s'. Here, p and s are called 'Extremes' and q and r are called 'Means'.
Consider the given question 4, 16 and 7
It can be written in proportional as
\[ \Rightarrow \,\,4:16::7:x\]
Where x is a 4th proportional which you can find that value.
 Proportion can be written in the ratio form, then
\[ \Rightarrow \,\,\dfrac{4}{{16}} = \dfrac{7}{x}\]
Divide both numerator and denominator of LHS by 4, then
\[ \Rightarrow \,\,\dfrac{1}{4} = \dfrac{7}{x}\]
On cross multiplying, we get
\[ \Rightarrow \,\,1 \times x = 7 \times 4\]
On simplification, we get
\[ \Rightarrow \,\,x = 28\]
Hence the 4th proportional of 4, 16 and 7 is 28.

Hence the correct answer is option ‘A’.

Note: Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Proportion is an equation which defines that the two given ratios are equivalent to each other. In the ratio and proportion the parameters are interlinked to each other.