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!. What is the value of 'C'?
Answers
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.