Question

If $ (30+x):(23+x)=5:4 $ then find the value of $ x $ .
A. $ 5 $
B. $ 6 $
C. $ 4 $
D. $ 7 $

Answer 1

Hint: The value of the ratio $ A:B $ is the quotient $ A/B $ . As the two given ratios are equivalent, so they would have the same value. Therefore to find the value of $ x $ from the given equation we have to compare left hand side with right hand side. Also use the BODMAS rule to solve the above equation step by step, as it also reduces the chances of any calculation mistake.

Complete step-by-step answer:
Ratio is the quantitative relation between the amounts showing the number of times one value contains or is contained within the other whereas in mathematics a ratio indicates how many times one number contains another.
As value of the ratio $ A:B $ is the quotient $ A/B $
So, $ (30+x):(23+X)=5:4 $ would become $ \dfrac{(30+x)}{(23+x)}=\dfrac{5}{4} $ .
Now when we compare left hand side to right hand side it, we can cross multiply on both sides.
So,
 $ \dfrac{(30+x)}{(23+x)}=\dfrac{5}{4} $
 $ 4(30+x)=5(23+x) $
Now by using the BODMAS (Bracket, Order, Division, Addition and subtraction) rule,
we solve the brackets first in the above equation.
So,
 $\Rightarrow 4(30+x)=5(23+x) $
 $\Rightarrow 120+4x=115+5x $
Now, take all the x terms to one side and constants to the other side.
So,
 $\Rightarrow 120+4x=115+5x $
 $\Rightarrow 120-115=5x-4x $
Now by simplifying the equation,
 $\Rightarrow 120-115=5x-4x $
 $\Rightarrow 5=x $ .
Now by comparing left hand side to right hand side we would get the value of x.
The value of x in the following equation is option (A) 5.
So, the correct answer is “Option A”.

Note: Thus to find the value of $ x $ we have to compare left hand side with right hand side and $ A:B $ can be written as $ A/B $ . After the cross multiplication take all the x terms towards one side and constants on the other side. Use the BODMAS rule to solve the following equation step by step.