Question

A Fraction becomes 4/5, if 1 is added to both the numerator and the denominator. If 5 is subtracted from both numerator and denominator the fraction becomes 1/2. Taking original Fraction as a/b. (i). Write a Mathematical statement for first condition. ​

Answer 1

Let the fraction be $\sf{{\dfrac{x}{y}}}$

⇒ $\sf{{\dfrac{x+1}{y+1}} = {\dfrac{4}{5}}}$

5x + 5 = 4y + 4

⇒ 5x - 4y = - 1 ───── ( 1 )

$\sf{{\dfrac{x-5}{y-5}}={\dfrac{1}{2}}}$

⇒ 2x - 10 = y - 5

⇒ 2x - y = 5 ───── (2)

[ y = 2x - 5 ]

Substitute the value of y in eqn. ( 1 )

5x - 4 ( 2x - 5 ) = - 1

⇒ 5x + 20 - 8x = - 1

⇒ x = 7

Put the value of x in eqn. (2)

y = 2 × 7 - y = 5

⇒ y = 9

$\sf{{\dfrac{x}{y}} = {\dfrac{7}{9}}}$