Question

If+the+numerator+of+a+fraction+is+multiplied+by+4+and+the+denominator+is+reduced+by+2,+the+result+is+2.+If+the+numerator+of+the+fraction+is+increased+by+15+and+2+is+subtracted+from+the+double+of+the+denominator+,+the+result+is9/7.+Find+the+fraction

Answer 1

Answer:

let the numerator be 'x' and denominator be 'y'

A.T.Q,

$\frac{4x}{y - 2} = 2 \\ \frac{x + 15}{2y - 2} = \frac{9}{7}$

cross multiplying both the equations we get,

2(y-2)=4x

4x-2y+4=0 {1}

9(2y-2)=7(x+15)

7x-18y+123=0 {2}

by elimination method,

(4x-2y+4)7=28x-14y+28 {3}

(7x-18y+123)4=28x-72y+492 {4}

subtracting {3} from {4} we get,

-58y+464=0

y=-464/-58

y=8

substituting this value in {1} we get,

4x-2(8)+4=0

4x=12

x=3.

the original fraction is

$\frac{3}{8}$