A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to denominator. Find the fraction. ( cross multiplication method)
Answers
Answer:
fraction = 5/12.
Step-by-step explanation:
Let us assume x/y as the fraction.
(i)first case: when 1 is subtracted from numerator.
x-1/y =1/3
3 (x-1)=y
3x-3=y
3x-y-3=0------ (1)
(ii)second case: when 8 is added to denominator.
x/(y+8)= 1/4
4x=y+8
4x-y-8=0------ (2)
(1) - (2) we get,
3x-4x-3+8=0
-x+5=0
x=5 ------ (3)
Sub (3) in (1),
4 (5)-y-8=0
20-y-8=0
y=12
Required fraction is 5/12.
Tq.
Answer:
5/12
Step-by-step explanation:
(i)first case: when 1 is subtracted from numerator.
x-1/y =1/3
3 (x-1)=y
3x-3=y
3x-y-3=0------ (1)
(ii)second case: when 8 is added to denominator.
x/(y+8)= 1/4
4x=y+8
4x-y-8=0------ (2)
this is the important part
a1=3,a2=4,b1=-1,b2=-1,c1=-3,c2=-8
a1/a2 not equal to b1/b2
so there must be a solution
x/b1 c2 − b2 c1 = y/c1 a2 − c2 a1 = 1/b2 a1 − b1 a2
x/5=y/12=1
x=5
y=12
therefore the required fraction is 5/12