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
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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
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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
[tex]\sf \dashrightarrow \dfrac{y}{y + 11}[/tex]
According to the question,
[tex]\sf \dashrightarrow \dfrac{y + 4}{(y + 11) - 1} = \dfrac{3}{5}[/tex]
[tex]\sf \dashrightarrow 5(y + 4) = 3(y + 11 - 1)[/tex]
[tex]\sf \dashrightarrow 5(y + 4) = 3(y + 10)[/tex]
[tex]\sf \dashrightarrow 5y + 4 = 3y + 30[/tex]
[tex]\sf \dashrightarrow 5y - 3y = 30 - 4[/tex]
[tex]\sf \dashrightarrow 2y = 26[/tex]
[tex]\sf \dashrightarrow y = \dfrac{26}{2}[/tex]
[tex]\sf \dashrightarrow y = 13[/tex]
Now, let's workout for the numerator and denominator of the fraction.
numerator of the fraction :
[tex]\sf \dashrightarrow y = 13[/tex]
Denominator of the fraction :
[tex]\sf \dashrightarrow y + 11[/tex]
[tex]\sf \dashrightarrow 13 + 11[/tex]
[tex]\sf \dashrightarrow 24[/tex]
So, the fraction becomes.
[tex]\sf \dashrightarrow Original \: fraction = \dfrac{13}{24}[/tex]
Hence, the original rational number is 13/24.