Question

In the ratio \[7:8\], if the consequent is 40, what is the antecedent?

Answer 1

Hint: Here in this question, we have to find the antecedent at when the consequent is 40 of the given ratio \[7:8\]. For this first we need to multiply x to the both consequent and antecedent of the given ratio then equate the consequent with 40 and find out the value of x. Next substitute the x value in antecedent and on further simplification to get the required antecedent.

Complete step-by-step answer:
Ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division. Or The division or fraction of the first quantity and second quantity is called ratio.
If the ratio of a and b can be expressed as \[a:b\] or \[\dfrac{a}{b}\].
The first quantity of the ratio is called antecedent whereas the second quantity of the ratio is called consequent.
Consider the given ratio:
\[7:8\] ----(1)
Here 7 is the antecedent and 8 is the consequent.
We need to find the antecedent at the consequent is 40.
Let’s multiply x to the both consequent and antecedent of the given ratio:
\[ \Rightarrow 7x:8x\] -----(2)
Now, equate the antecedent with 40, then
\[ \Rightarrow 8x = 40\]
Divide both side by 8, then we have
\[ \Rightarrow x = \dfrac{{40}}{8}\]
\[ \Rightarrow x = 5\]
Substitute the value \[x = 5\] in antecedent of (2), then we get
\[ \Rightarrow 7\left( 5 \right)\]
\[\therefore 35\]
Therefore, In the ratio \[7:8\], if the consequent is 40 then will antecedent become 35.
Hence, the required ratio is \[35:40\]
So, the correct answer is “Option B”.

Note: If any number multiplied with both antecedent and consequent of any ratio the value of remain unchanged the resultant ratio called as equivalent ratio. If we verify the ratios . The ratios are equivalent means it should satisfies the condition and it is given as \[\dfrac{a}{b} = \dfrac{c}{d} \Leftrightarrow ad = bc\], where the a, b, c and d are the real values.