Question

if the numerator of a fraction is decreased by 1 its value becomes 2 by 3 but if the denominator is increased by 5 its value becomes 1 by 2 what is a fraction​

Answer 1

Answer :-

♦ As given in the question :-

If numerator is decreased by 1 fraction

= $\dfrac{2}{3}$

If denominator is increased by 5 fraction

= $\dfrac{1}{2}$

♦ Let the

• Numerator be "x"

• Denominator be "y"

♦ Then from above equation becomes

$\dfrac{x-1}{y} = \dfrac{2}{3}$ ....(i)

and

$\dfrac{x}{y + 5} = \dfrac{1}{2}$ .....(ii)

♦ Then by cross multiplication equation

(i) $\implies 3(x-1) = 2(y)$

$\implies 3x - 3 = 2y$

$\implies 3x - 2y = 3$ ..... (iii)

(ii) $\implies 2(x) = (y+5)$

$\implies 2x = y+5$

$\implies 2x - y = 5$ .....(iv)

♦ Now by subtracting 2 times equation (iv) from equation (iii)

$3x - 2y = 3$ - $2( 2x - y) = 2(5)$

$\implies 3x - 2y = 3$ $-( 4x - 2y )= 10$

$3x - 2y = 3$

$- 4x + 2y = - 10$

_______________________

$-x + 0 = -7$

♦ Then value of x = 7

♦ By putting value of "x' in equation (iii)

$3x - 2y = 3$

$\implies 3(7) - 2y = 3$

$\implies 21 - 2y = 3$

$\implies - 2y = 3 - 21$

$\implies - 2y = -18$

$\implies y = \dfrac{-18}{-2}$

$\implies y = 9$

♦ So value of

Numerator = 7

Denominator = 9

So fraction = $\dfrac{7}{9}$

Answer 2

Answer:

7/9

Step-by-step explanation: