the denominator of a rational no is greater than its numerator by 7 if the numerator is - Maths - Linear Equations in One Variable

Question

the denominator of a rational no is greater than its numerator
by 7 if the numerator is increased by 17 and the denominator is
decreased by 6, the new number becomes 2 fin the original
number

Lalit Mehra · Accepted Answer

Dear Student!

Let the numerator of the rational number be x.

Given, Denominator = Numerator + 7

∴ Denominator of the rational number = x + 7

$∴ Fraction = \frac{Numerator}{Denominator} = \frac{x}{x + 7}$

When numerator is increased by 17 and denominator is decreased by 6, the fraction becomes 2.

$∴ \frac{x + 17}{(x + 7) - 6} = 2 \Rightarrow \frac{x + 17}{x + 1} = 2 \Rightarrow x + 17 = 2 (x + 1) \Rightarrow x + 17 = 2 x + 2 \Rightarrow x - 2 x = 2 - 17 \Rightarrow - x = - 15 \Rightarrow x = 15$

Original fraction $= \frac{x}{x + 7} = \frac{15}{15 + 7} = \frac{15}{22}$

Cheers!

the denominator of a rational no. is greater than its numerator by 7. if the numerator is increased by 17 and the denominator is decreased by 6, the new number becomes 2. fin the original number.