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