Question

The numerator of a fraction is 3 less than its denominator if 1 is added to the denominator the fraction is decreased by 1/5 find the fraction

Answer 1

CORRECT QUESTION

The numerator of a fraction is 3 less than

it's denominator if 1 is added to the denominator

the fraction is decreased by 1/15 find the fraction

EXPLANATION

Let the denominator of a required fraction = x

Numerator of the required fraction = x - 3

original fraction = x - 3 / x

GIVEN

If 1 is added to the denominator the fraction is

decreased by 1/15

new fraction = x - 3 / x + 1

According to the question

x - 3/ x + 1 = x - 3 / x - 1/15

x - 3 / x - x - 3/x + 1 = 1/15

(x - 3 ) (x + 1) - x ( x - 3) /x(x + 1) = 1/15

x^2 + x - 3x - 3 - x^2 + 3x/x^2 + x = 1/15

x - 3 / x^2 + x = 1/15

x^2 + x =15x - 45

x^2 - 14x + 45 = 0

x^2 - 9x - 5x + 45 = 0

x( x - 9 ) -5 ( x - 9 ) = 0

( x - 5 ) ( x - 9 ) = 0

x = 5 and x = 9

if x = 5

x - 3 / x = 5 - 3 / 5 = 2/5

if x = 9

x - 3 /x = 9 - 3/9 = 2/3

this fraction is not satisfy the condition

Hence required fraction be = 2/5