Question

If the numerator and denominator of a certain fraction are increased by 2,the
fraction becomes 3/5. If numerator and denomenator are increased by 1,it becomes 1/2.find the fraction?

Answer 1

HI !

Let the numerator be x and the denominator be y.
the fraction would be x/y

given ,

$\frac{x+2}{y+2} = \frac{3}{5}$
cross multiply ,

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

5x + 10 = 3y + 6

5x - 3y = -4 ----> {1}

==========================================

also ,

$\frac{x+1}{y+1} = \frac{1}{2}$

cross multiply ,

2(x+1) = y + 1

2x + 2 = y + 1

2x - y = -1 ---> [2]

solving equations 1 and 2 by elimination method ,


2x - y = -1
5x - 3y = -4

2x - y = -1 = 3(2x - y = -1 )
= 6x - 3y =-3

6x - 3y =-3
- 5x - 3y = -4
==============
x = 1

2x - y = -1

2 - y = -1

y = 2 + 1 = 3

=================================

x = 1 , y = 3

the fraction is 1/3