A fraction is such that if numerator is multiply by 3 and the denominator is reduce by 2 we get 3/5 but if the numerator is increased by 4 and the denominator is doubled we get 5/14. Find the fraction.
Answers
EXPLANATION.
let the fraction be = x/y
Case = 1.
A fraction is such that if numerator is multiply
by 3 and the denominator is reduced by 2
we get = 3/5
=> 3x / y - 3 = 3/5
=> 5 ( 3x ) = 3 ( y - 3 )
=> 15x = 3y - 9
=> 15x - 3y = -9
=> 5x - y = -3 .......(1)
Case = 1.
if the numerator is increased by 4 and the
denominator is double we get = 5/14
=> x + 4 / 2y = 5/14
=> 14 ( x + 4 ) = 5 ( 2y )
=> 14x + 56 = 10y
=> 14x - 10y = -56
=> 7x - 5y = - 28 ......(2)
Find the fraction.
From equation (1) and (2) we get,
=> multiply equation (1) by 5
=> multiply equation (2) by 1
we get,
=> 25x - 5y = -15
=> 7x - 5y = -28
we get,
=> 18x = 13
=> x = 13/18
put the value of x = 13/18 in equation (1)
we get,
=> 5x - y = -3
=> 5 X 13/18 - y = -3
=> 65/18 - y = -3
=> -y = -3 - 65/18
=> -y = -54 - 65 / 18
=> -y = -119/18
=> y = 119/18