Question

If 1 is added to the numerator of a fraction , it becomes 15 ; and if 1 is subtracted from the denominator , it becomes 17 , find the fraction.

Answer 1

S O L U T I O N :

Let the numerator place be x & let the denominator place be y respectively.

$\boxed{\bf{The\:fraction = \frac{x}{y} }}$

A/q

$\underbrace{\bf{1^{st}\:Case\::}}$

$\mapsto\tt{\dfrac{x + 1}{y} = 15}$

$\mapsto\tt{x+1 = 15y}$

$\mapsto\tt{x = 15y- 1...............(1)}$

$\underbrace{\bf{2^{nd}\:Case\::}}$

$\mapsto\tt{\dfrac{x }{y-1} = 17}$

$\mapsto\tt{x = 17(y-1)}$

$\mapsto\tt{x = 17y-17}$

$\mapsto\tt{(15y-1) = 17y-17\:\:[from(1)]}$

$\mapsto\tt{15y-1 = 17y-17}$

$\mapsto\tt{15y-17y = -17+1}$

$\mapsto\tt{-2y = -16}$

$\mapsto\tt{y = \cancel{-16/-2}}$

$\mapsto\bf{y=8}$

∴ Putting the value of y in equation (1),we get;

$\mapsto\tt{x = 15(8) - 1}$

$\mapsto\tt{x = 120- 1}$

$\mapsto\bf{x = 119}$

Thus,

• Numerator = x = 119
• Denominator = y = 8

$\boxed{\bf{The\:fraction = \frac{x}{y} = \frac{119}{8} }}$