Question :
When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1 /4 . And, when 6 is added to numerator and the denominator is multiplied by 3 , it becomes 2 /3 . Find the fraction.Submitted on 8/3/2024 | Answered by Vandana Rana
Answer :
Let the numerator be
x
and denominator be
y
Then fraction =x/y
⇒
According to question
(x-2)/(y+3)=1/4
⇒
4
(
x
−
2
)
=
y
+
3
⇒
4
x
−
8
=
y
+
3
=>
4
x
−
y
=
11
........ 1
According to question
(x
+
6)/
3
y
=
2/
3
⇒
3
(
x
+
6
)
=
6
y
⇒
3
x
−
6
y
=
−
18
..............2
multipy
(
1
) by 6 and subtracting
−
(
2
)from it
21
x
=
84
x
=
4
Put. x = 4 in (1)
we get
y=7
fraction =4/7