Question

the numerator of a fraction exceeds the denominator by 5. If the numerator is decreased by 4 and the denominator is increased by 3, the resulting fraction is equal to 4/5. Find the origional fraction.

Answer 1

The original fraction is
`(12)/(7)` .

Explanation:

Given as :

Let The original fraction
`(x)/(y)`

where numerator = x

Denominator = y

Now, The statement are

The numerator exceed the denominator by 5

i.e numerator = 5 + denominator

Or, x = 5 + y ........1

Again

The numerator is decreased by 4 and the denominator is increased by 3, the resulting fraction is equal to 4/5.

So,

`(x - 4)/(y + 3)` =
`(4)/(5)`

Or, 5 × ( x- 4 ) = 4 × ( y + 3 )

Or, 5 x - 20 = 4 y + 12

Or, 5 x = 4 y + 12 + 20

Or, 5 x = 4 y + 32 ........2

Solving equation 1 and 2

Putting the value of x from eq 1 into eq 2

So, 5 × ( 5 + y ) = 4 y + 32

Or, 25 + 5 y = 4 y + 32

Or, 5 y - 4 y = 32 - 25

i.e, y = 7

So, The denominator = y = 7

Now,putting vale of y into eq 2

So, 5 x = 4 × 7 + 32

Or, 5 x = 28 + 32

Or, 5 x = 60

∴ x =
`(60)/(5)`

i.e x = 12

So, The numerator = x = 12

So fraction
`(x)/(y)` =
`(12)/(7)`

Hence, The original fraction is
`(12)/(7)` . Answer