Question

If 40% of a number is equal to two-third of another number, what is the ratio of the first number to the second number?
A). \[2:5\]
B). \[3:7\]
C). \[5:3\]
D). \[7:3\]

Answer 1

Hint: Assume the first number as \[A\] and the second number as \[B\]. Solve the \[\%\] sign by dividing the quantity by \[100\] and ‘of ’ is replaced with the multiplication sign. After that try to simplify the whole equation and give the final answer in terms of \[A\] ratio \[B\]. Now try to find out the answer by yourself.

Complete step-by-step solution:
The concept used in this question is of ratio and proportion. This concept is one of the basic fundamentals of mathematics. The only use of ratio is to compare the two quantities, that is by how much the first quantity is greater than the other one or by how much the first quantity is less than the other one. Or we can say that it is used to tell the relationship between the two quantities. The symbol used to represent the ratio is ‘ : ’ or we can also use the symbol ‘ / ’.Let us understand this with the help of an example,
If it is given that the ratio of \[A\] and \[B\] is \[3:1\]then this means that the value of \[A\] is \[3\]times greater than the value of \[B\].
Let us assume that the first number is \[A\] and the second number is \[B\]. Then the given question is represented mathematically as
\[40\%\text{ }of\text{ }A=\dfrac{2}{3}\text{ }of\text{ }B\]
To solve the sign of \[\%\]we have to divide the quantity by the number \[100\] and to solve ‘of ’ we have to replace it the multiplication sign, after applying this we will get
\[\Rightarrow \dfrac{40}{100}\times A=\dfrac{2}{3}\times B\]
Now further solve this equation we will get
\[\Rightarrow \dfrac{2}{5}\times A=\dfrac{2}{3}\times B\]
Cancel out \[2\]from both the sides, we will get
\[\Rightarrow \dfrac{1}{5}\times A=\dfrac{1}{3}\times B\]
To find the ratio of the first number to the second number we have to divide the whole equation from \[B\], then we will get
\[\Rightarrow \dfrac{1}{5}\times \dfrac{A}{B}=\dfrac{1}{3}\]
Further solve the expression to get the ratio of \[A\] and \[B\], we will get
\[\Rightarrow \dfrac{A}{B}=\dfrac{5}{3}\]
From this we can say that the ratio of \[A\] and \[B\] is \[5:3\].

Note: We can only find the relation between the two or more quantities using ratio if and only if they are in the same units. And if we multiply or divide individual terms of the ratio by the same quantity then there is no effect on the overall ratio that means they both are the same. For example, \[3:2\] and \[6:4\] both are the same.