Question

.A fraction becomes 1/3, if 2 is added to both numerator and denominator .If 3 is added to both numerator and denominator it becomes 2/5 . Find the fraction.

Answer 1

Let numerator= x
Let denominator= y

ATQ    x+2/y+2=1/3
           3x+6=y+2
            y=3x+4..........(i)

x+3/y+3=2/5
5x+15=2y+6

Putting  (i)
5x+15=2(3x+4)+6
15=6x+8+6
1=6x
x=1/6

Putting x in (i)
y=3(1/6)+4
y=1/2+4
y=1+8/2
y=9/2

Fraction= x/y=1/6 / 9/2
1/6*2/9=1/27

Answer 2

The value of x = 1 and y=7

Given:

$\frac {x+2} {y+2} = \frac {1}{3}$

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

To find:

The values “x” and “y”

Answer:

Assume denominator is x

Denominator is y

$\frac {x+2} {y+2} = \frac {1}{3}$

$3x + 6 = y + 2$

$3x - y + 4=0$

$x = \frac {y-4} {3} ... (1)$

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

$5x + 15 = 2y + 6$

$5x - 2y + 9 = 0 ....(2)$

Substitute equation 1 in 2

$\frac { 5 \times (y-4)}{3} - 2y + 9 = 0$

$\frac { 5 \times y - 20 - 6 \times y + 27 }{3} = 0$

$- y + 7 = 0$

$y = 7$

Substitute y value in equation 1

$x = \frac {7-4} {3}$

$x = \frac {3}{3}$

$x = 1$