Question

If \[1.5x = 0.04y\], then value of \[\dfrac{{y - x}}{{y + x}}\] is equal to
A) \[0.236\]
B) \[0.437\]
C) \[0.784\]
D) \[0.948\]

Answer 1

Hint:
Here we will first find the value of \[y\] in terms of \[x\] by using the given equation. Then we will put this value of \[y\] in the expression and solve it. Then by solving the equation we will get the value of the required equation i.e. \[\dfrac{{y - x}}{{y + x}}\].

Complete Step by step Solution:
The given equation is \[1.5x = 0.04y\].
First, by using the above equation we will find the value of \[y\] in terms of \[x\]. Therefore, we get
\[ \Rightarrow y = \dfrac{{1.5x}}{{0.04}}\]
Now by using the simple division operation we will get the desired relation between \[x\] and \[y\]. Therefore, we get
\[ \Rightarrow y = 37.5x\]
Now we will find the value of \[\dfrac{{y - x}}{{y + x}}\] by simply putting the value of the \[y\] in terms of \[x\] in this equation to get its value. Therefore, we get
\[ \dfrac{{y - x}}{{y + x}} = \dfrac{{37.5x - x}}{{37.5x + x}}\]
\[ \Rightarrow \dfrac{{y - x}}{{y + x}} = \dfrac{{36.5x}}{{38.5x}}\]
Now the \[x\] get cancelled out as it is in the numerator and the denominator as well. Therefore, we get
\[ \Rightarrow \dfrac{{y - x}}{{y + x}} = \dfrac{{36.5}}{{38.5}}\]
Now by simply using the division operation in the above equation, we get
\[ \Rightarrow \dfrac{{y - x}}{{y + x}} = 0.948\]
Hence the value of \[\dfrac{{y - x}}{{y + x}}\] is equal to \[0.948\].

So, option D is the correct option.

Note:
We have solved the question, using the substitution method. Here it is not necessary that we take value of the \[y\] in terms of \[x\] we can also take \[x\] in terms of \[y\] and solve it further in the same way. This question involves basic mathematical operations like addition, subtraction, and division. The addition is the operation in which two numbers are combined to get the result. Subtraction is the operation which gives us the difference between the two numbers. The division is the operation in which the dividend is divided by the divisor to get the quotient along with some remainder.