Question

B. The denominator of a rational number is greater than its numerator by 11. If the numerator is 3 increased by 4 and the denominator is decreased by 1, the number obtained is 3/5 Find the rational number​

Answer 1

Answer

We know that,

The denominator of a fraction exceeds the numerator by 11.

If 4 is added to numerator and the denominator is decreased by 1, the fraction obtained is ⅗.

Let the numerator be y.

Let the denominator be y + 11.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{y}{y + 11}$

According to the question,

$\sf \dashrightarrow \dfrac{y + 4}{(y + 11) - 1} = \dfrac{3}{5}$

$\sf \dashrightarrow 5(y + 4) = 3(y + 11 - 1)$

$\sf \dashrightarrow 5(y + 4) = 3(y + 10)$

$\sf \dashrightarrow 5y + 4 = 3y + 30$

$\sf \dashrightarrow 5y - 3y = 30 - 4$

$\sf \dashrightarrow 2y = 26$

$\sf \dashrightarrow y = \dfrac{26}{2}$

$\sf \dashrightarrow y = 13$

Now, let's workout for the numerator and denominator of the fraction.

numerator of the fraction :

$\sf \dashrightarrow y = 13$

Denominator of the fraction :

$\sf \dashrightarrow y + 11$

$\sf \dashrightarrow 13 + 11$

$\sf \dashrightarrow 24$

So, the fraction becomes.

$\sf \dashrightarrow Original \: fraction = \dfrac{13}{24}$

Hence, the original rational number is 13/24.