Question

A fraction becomes 8/9 if 1 is added to both numerator and denominator,if however 5 is subtracted from numerator&denominator the fraction becomes 2/3 .What is the fraction?

Answer 1

Given,

A fraction becomes 8/9 if 1 is added to both numerator and denominator.

And,when 5 is subtracted from numerator&denominator the fraction becomes 2/3 .

To find,

The actual fraction.

Solution,

Let,the numerator of the fraction = x

And,the denominator of the fraction = y

[Assume, x and y as variables to do the further mathematical calculations.]

So,the fraction = numerator/denominator = x/y

According to the question,

(x+1)/(y+1) = 8/9

9x+9 = 8y+8

9x = 8y-1

x = (8y-1)/9 .......(1)

And,

(x-5)/(y-5) = 2/3

3x-15 = 2y-10

3x = 2y+5

x = (2y+5)/3 ......(2)

By, comparing (1) and (2),we get that,

(8y-1)/9 = (2y+5)/3

24y-3= 18y+45

6y = 48

y = 8

By putting the value of y in (1),

x = (8×8-1)/9

x = (64-1)/9

x = 63/9

x = 7

Hence,the actual fraction is 7/8.