Question

the denominator of a ratiinal number is greater than its numerator by 7. if the numerator is increased by 13 and denominator is decreased by 2 , rh number obtauned is 4/3. find the rational number​

Answer 1

Correct Question

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 13 and denominator is decreased by 2 , the number obtained is 4/3. find the original rational number.

Answer

Let the numerator of the fraction be y.

Let the denominator of the fraction be y + 7.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{y}{y + 7}$

According to the question,

The numerator is increased by 13 and the denominator is decreased by 2.

So, the fraction becomes

$\sf \dashrightarrow \dfrac{y + 13}{(y + 7) -2}$

We have also given with a fraction that will occur to us when some of the numbers will be removed or added to numerator and denominator. That fraction is,

$\sf \dashrightarrow \dfrac{4}{3}$

Numerator of the fraction :

Now, as we know that

$\sf \dashrightarrow \dfrac{y + 13}{(y + 7) - 2} = \dfrac{4}{3}$

Cross multiply the numbers.

$\sf \dashrightarrow 3 (y + 13) = 4 (y + 7 - 2)$

$\sf \dashrightarrow 3y + 39 = 4y + 28 - 8$

$\sf \dashrightarrow 3y - 4y = 28 - 8 - 39$

$\sf \dashrightarrow -1y = 20 - 39$

$\sf \dashrightarrow -1y = - 19$

$\sf \dashrightarrow y = \dfrac{-19}{-1}$

$\sf \dashrightarrow y = 19$

Now, we should work-out for the denominator of the fraction.

Denominator of the fraction :

$\sf \dashrightarrow 19 + 7$

$\sf \dashrightarrow 26$

So, the original fraction becomes

$\sf \dashrightarrow \dfrac{19}{26}$

Hence, the original fraction is $\sf \dfrac{19}{26}$.