Question

If we have the ratios as $m:30::2:12$ then the value of m is __
A). 2
B). 12
C). 1
D). 5

Answer 1

Hint- The above equation can be solved by using the concept of ratio and proportion. The given numbers are in proportion which means that the ratio of the first two quantities must be equal to the ratio of the second quantities. Using this relation we will solve the question to get the answer.

Complete step-by-step solution -
Let a, b, c and d are proportional and the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., a : b : : c : d
When the terms are in proportion, then they are called proportional to each other. The first and the last terms are referred to as extremes, while the second and third terms are referred to as means. For example – if a, b, c and d are in proportion then a and d are known as extreme terms and b and c are called middle terms.
Also the product of mean terms is always equal to the product of extreme terms. i.e. \[a:b::c:d\]
if and only if ad = bc
The given equation is $m:30::2:12$
This equation can be expressed in terms of fraction as
$\dfrac{m}{{30}} = \dfrac{2}{{12}}$
Now solving the above equation for finding the value of m, we get
\[
   \Rightarrow \dfrac{m}{{30}} = \dfrac{2}{{12}} \\
   \Rightarrow m = 30 \times \dfrac{2}{{12}} \\
   \Rightarrow m = 5 \\
\]
Therefore the value of m is 5.
Hence, the correct option is D.

Note- In order to solve these types of questions, remember the concept of proportion and the methods of solving linear equations with single variables. The linear equations in one variable are written as $ax+b =c$ where a, b and c are constants. These equations are first degree equations.