Question

A fraction will be equal to 4/5 if 1 is added to both numerator and denominator.if ,however,5 is subtracted from both numerator and denominator, the fraction will be equal to 1/2.find the fraction
With full process

Answer 1

let numerator be x and denominator be y.
A/C

x+1/y+1=4/5
5x+5=4y+4
x=(4y-1)/5
now when subtracted
x-5/y-5=1/2
2x-10=y-5
2(4y-1)/5-10=y-5
(8y-2)/5=y+5
8y-2=5y+25
3y=27
y=9
so x=(4y-1)/5
=4×9-1/5
=36-1/5
=35/5=7
so the fraction is x/y=7/9

Answer 2

Given - Ratio on addition and subtraction

Find - Fraction

Solution - The fraction is 7/9.

Let the fraction be x/y. Forming first as per the first statement.

x+1/y+1 = 4/5 Equation 1

Solving the above-mentioned equation -

5x + 5 = 4y + 4

Performing subtraction -

5x = 4y + 4 - 5

5x = 4y - 1

x = (4y - 1)/5 Equation 2

Forming equation as per the second statement.

x - 5/y - 5 = 1/2 Equation 3

Solving the above-mentioned equation -

2x - 10 = y - 5

Keeping the value of x from equation 2

2x = y + 5

2(4y - 1)/5 = y + 5

Performing cross multiplication

8y - 2 = 5y + 25

Performing subtraction

3y = 27

y = 9

Finding the value of x

x = (4y - 1)/5

Keeping the value of y and performing subtraction

x = (4*9 - 1)/5

x = (36 - 1)/5

x = 35/5

x = 7

So, the fraction is 7/9.