Question

the denominator of a rational number is greater than its numerator by 5 is the numerator and denominator are decreased by 15 and 1 respectively the number obtained is 3/2. find the rational number.

Answer 1

GIVEN,

ACCORDING TO THE QUESTION,

LET THE NUMERATOR BE "X"

HENCE, DENOMINATORS WILL BE "X + 5"

RATIONAL NO.= $\dfrac {x}{x+5}$

WHEN NUMERATOR AND DENOMINATOR ARE DECREASED BY 15 AND 1 RESPECTIVELY,

$\dfrac {x - 15}{x + 5 - 1}$ = $\dfrac {3}{2}$

BY CROSS MULTIPLYING,

$\dfrac {x-15}{x+4}$ × $\dfrac {3}{2}$

2x - 30 = 3x + 12

3x - 2x = -30-12

x = -42

HENCE NUMERATOR = -42
HENCE DENOMINATOR = -42+5 = -37

Rational number = $\dfrac {-42}{-37}$