Question

Q30 The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator
is decreased by 1, the number obtained is 3/2. Find the rational number.​

Answer 1

Answer:

i hope it will help you all

Answer 2

Answer:

The original rational number is $\sf{\dfrac{13}{21}}$

Step-by-step explanation:

Denominator = 8 more than numerator

In the original Rational number:

• Numerator = y
• Denominator = (y + 8)

According to the question,

$\sf{\longrightarrow} \: \dfrac{y + 17}{(y + 8) - 1} = \dfrac{3}{2}$

$\sf{\longrightarrow} \: \dfrac{y + 17}{y + 7} = \dfrac{3}{2}$

$\sf{\longrightarrow} \: 2(y + 17) = 3(y + 7)$

$\sf{\longrightarrow} \: 2y + 34 = 3y + 21$

$\sf{\longrightarrow} \: 2y - 3y = 21 - 34$

$\sf{\longrightarrow} \: - y = - 13$

$\sf{\longrightarrow} \: y = 13$

Numerator = 13

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Denominator =

$\sf{\longrightarrow} \: 13 + 8$

$\sf{\longrightarrow} \: 21$

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Original Rational number:

$\sf{\longrightarrow} \: \dfrac{13}{21}$

Therefore, the original rational number is $\sf{\dfrac{13}{21}}$