Step-by-step explanation:

GIVEN:-

The DIFFERENCE between two numbers 'A' and 'B' is 30. 'A' is 12.5% more than a third number 'C' and 'B'is 25% less than C.

To find:-

What is the value of 'C'?

SOLUTION:-

Given numbers are A , B and C

The difference between two numbers 'A' and 'B' is 30.

A- B = 30---------(1)

'A' is 12.5% more than a third number 'C'

=>A = C + 12.5 % of C

=> A = C +(12.5/100)× C

=> A = C +(12.5C/100)

=> A = (100 C +12.5C)/100

=> A = 112.5 C/100----------(2)

and 'B' is 25% less than C.

=> B = C -(25% of C)

=> B = C -(25/100)×C

=> B = C -(25C/100)

=> B = (100C -25C)/100

=> B = 75C/100 -----------(3)

On Substituting the values of A and B in the EQUATION (1) then

=> A - B = 30

=> (112.5C/100) - ( 75C/100) = 30

=> (112.5C -75C)/100 = 30

=> 37.5C /100 = 30

=>37.5 C = 30×100

=> 37.5C = 3000

=> 375C/10 = 3000

=> 375C = 3000×10

=> 375C = 30000

=> C = 30000/375

=> C = 80

Therefore, C = 80

Answer:-

The value of C for the given problem is 80

Check:-

C = 80

A = 112.5C/100

=> A = 112.5×80/100

=> A = 112.5×8/10

=> A = 900/10

=> A = 90

And B = 75C/100

=> B = 75×80/100

=> B = 6000/100

=> B = 60

The difference between A and B =

=> 90-60

=> 30

Verified the given relations.