A fraction becomes ½ if 1 is added to the number. It will again become 6/11 if 3 is added to both
numerator and denominator . Find fraction
Answers
Step-by-step explanation:
Correction :-
A fraction becomes ½ if 1 is added to the numerator
Given:-
A fraction becomes ½ if 1 is added to the numerator. It will again become 6/11 if 3 is added to both numerator and denominator .
To find:-
Find the fraction ?
Solution:-
Let the numerator be X
Let the denominator be Y
Then ,the fraction = X/Y
If 1 is added to the numerator then it becomes 1/2
=> (X+1)/Y = 1/2
On applying Cross multiplication then
=> 2(X+1) = Y×1
=> 2X+2 = Y
Y = 2X+2 ---------------(1)
If 3 is added to both numerator and the denominator it becomes 6/11
=>(X+3)/(Y+3) = 6/11
On applying Cross multiplication then
=> 11(X+3) = 6(Y+3)
=> 11X+33 = 6Y +18
=>11 X +33 = 6(2X+2)+18
(from (1))
=> 11X+33 = 12X+12+18
=> 11X+33 = 12X+30
=> 12X-11X = 33-30
=> X = 3
On substituting the value of X in (1)
Y = 2(3)+2
=> Y = 6+2
=>Y = 8
Therefore, X = 3 and Y = 8
Answer:-
The required fraction for the given problem is 3/8
Check:-
The fraction = 3/8
If 1 is added to numerator then
=> (3+1)/8
=> 4/8
=> 1/2
If 3 is added to both the numerator and the denominator then
=> (3+3)/(8+3)
=> 6/11
Verified the given relations in the problem.