Equivalent Ratios

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Equivalent ratios are basically defined as the two equivalent ratios. For example, a/b and c/d are said to be equivalent ratio if and only if a/b = c/d. This is really advantageous in finding out the value of one unknown variable when the ratios are equivalent and other parameters are also given. This type of ratio generally use cross multiplication concept to evaluate the unknown variable. This can be better clarified by taking the suitable examples and the examples are as follows:-

Question 1:- If the following relation holds: (x+8) /20 = 400/20 then evaluate the value of x.

Solution 1:- Given (x+8)/20 = 400/20

Step 1:- First let us solve Right hand side (x+8)/20 = 20

Step 2:- Now solving the above expression by cross multiplication,
                        (x+8) = 20 *20
                        (x+8) = 400

Step 3:- To evaluate the value of x, subtract 8 from both sides,
                        (x+8-8) = 400 -8

So the value of x = 392
 
Question 2:- If (2x-4)/4 = (x+4)/16

Solution 2:- Given expression is:- (2x-4)/4 = (x+4)/16

Step 1:- In this problem, to evaluate the value of x, we need to cross multiply first.

So 16 (2x-4) = 4 (x+4)

On solving,

32x -64 = 4x + 16

32x -4x = 64 + 16

28 x = 80

Step 2:- Now to evaluate the value of x, we need to divide both sides by 28

Therefore 28x/28 = 80/28

So x = 80/28

On dividing,

We get x = 2.86  as the final answer.

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