Question

uc ages will be 3:4. Find their present ages.
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
3
obtained is
2
Find the rational number.​

Answer 1

Answer:-

Let the fraction be x/y.

Given:-

Denominator is greater than the numerator by 8.

⟹ y = 8 + x -- equation (1).

Also given that,

If the numerator is increased by 17 , and denominator is decreased by 1 , the number obtained is 3/2.

According to the above condition,

$\implies \sf \: \dfrac{x + 17}{y - 1} = \frac{3}{2}$

Substitute the value of y from equation (1).

$\implies \sf \: \frac{x + 17}{x + 8 - 1} = \frac{3}{2} \\ \\ \\ \implies \sf \:2(x + 17) = 3(x + 7) \\ \\ \implies \sf \:2x + 34 = 3x + 21 \\ \\ \\ \implies \sf \:34 - 21 = 3x - 2x \\ \\ \\ \implies \boxed{\sf \:13 = x}$

Substitute the value of x in equation (1).

⟹ y = 8 + x

⟹ y = 8 + 13

⟹ y = 21

∴ The required fraction x/y is 13/21.

Answer 2

Answer:

Correct Question :-

• 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.

Given :-

• 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.

To Find :-

• What is the rational number.

Solution :-

Let, the numerator be x

And, the denominator will be x + 8

Then, the rational number is $\sf \dfrac{x}{x + 8}$

According to the question,

↦ $\sf \dfrac{x + 17}{x + 8 - 1} =\: \dfrac{3}{2}$

↦ $\sf \dfrac{x + 17}{x + 7} =\: \dfrac{3}{2}$

By doing cross multiplication we get,

↦ $\sf 3(x + 7) =\: 2(x + 17)$

↦ $\sf 3x + 21 =\: 2x + 34$

↦ $\sf 3x - 2x =\: 34 - 21$

➠ $\sf\bold{\pink{x =\: 13}}$

Now, we have to find the rational number :

$\implies$ $\sf \dfrac{x}{x + 7}$

$\implies$ $\sf \dfrac{13}{13 + 8}$

$\implies$ $\sf\boxed{\bold{\dfrac{13}{21}}}$.

$\therefore$ The rational number is $\sf\bold{\dfrac{13}{21}}$.