Question

if 4 is subtracted from the numerator of a fraction its value becomes 1/3 if 5 is added to the denominator of the original fraction its value becomes 1/2 what is the original fraction​

Answer 1

Answer:

7/9

Step-by-step explanation:

let the numerator be x and denominator be y

when 4. is subtracted

x-4/y=1/3

3x-12=y

3x-y=12

x/y+5=1/2

2x=y+5

2x-y=5

by elimination method

x=7

substituting x =7 in 2x-y=5

2×7-y=5

14-y=5

-y=5-14

-y =-9

y=9

therefore the fraction is x/y

=7 /9

.

Answer 2

Step-by-step explanation:

Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes x\y

According to the question,

Condition I,

If 4 is subtracted from the numerator of a fraction, its value becomes 1/3.

or,x−4\ y=1\3

or,3(x−4)=y

or,y=3x−12

Condition II,

If 5 is added to the denominator of the original fraction, the value becomes 1/2.

or,x\y+5=1\2

or,2x=y+5

Put value of y from equation (i) in equation (ii), we get,

or,2x=(3x−12)+5

or,2x=3x−12+5

or,3x−2x−7=0

∴x=7

Put value of x in equation (i), we get,

or,y=3×7−12

or,y=21−12

y=9

So, (x,y) = (7,9)

thus, the required original fraction is 7\ 9.