Question

the addition of numerator and denominator of a fraction is 3 less than twice the denominator if the numerator and denominator are decreased by 1 the numerator become half the denominator find the fraction​

Answer 1

• Let Numerator be x

And

• Denominator be y.

So, fraction = $\dfrac{x}{y}$

» A.T.Q.

Addition (sum) of Numerator and Denominator of a fraction is 3 less than twice the Denominator.

=> x + y = 2y - 3

=> x = 2y - y - 3

=> x = y - 3 __(1)

• Now

If Numerator and Denominator are decreased by 1 [(x - 1)/(y - 1)]. The Numerator becomes half the Denominator.

=> $\dfrac{x\:-\:1}{y\:-\:1}$ = $\dfrac{y}{2y}$

=> $\dfrac{x\:-\:1}{y\:-\:1}$ = $\dfrac{y}{2y}$

=> $\dfrac{x\:-\:1}{y\:-\:1}$ = $\dfrac{1}{2}$

=> x - 1 = $\dfrac{y\:-\:1}{2}$

=> x - 1 = $\dfrac{y\:-\:1}{2}$

=> x = $\dfrac{y\:-\:1}{2}$ + 1

=> x - 1 = $\dfrac{y\:-\:1}{2}$

=> x = $\dfrac{y\:-\:1}{2}$ + 1

=> x = $\dfrac{y\:-\:1}{2}$ + $\dfrac{1}{1}$

=> x = $\dfrac{y\:-\:1\:+2}{2}$

=> x = $\dfrac{y\:-\:1\:+2}{2}$

=> x = $\dfrac{y\:+\:1}{2}$

=> 2x = y + 1

=> 2(y - 3) = y + 1 [From equation (1)]

=> 2y - 6 = y + 1

=> 2y - y = 1 + 6

=> y = 7 __(2)

Put value of y in equation (1)

=> x = (7) - 3

=> x = 7 - 3

=> x = 4 __(3)

Fraction = $\dfrac{x}{y}$

- ________[ANSWER]

$\dfrac{x}{y}$ = $\dfrac{4}{7}$