Question

The denominator of a rational no. Is greater than its numerator by 8
Tf the numerator is increased by 17 and the denominator is decreased
by 1, the rumber obtained is3/2 find the rational numberليا​

Answer 1

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 :

• The rational number.

Solution :

Consider,

• Numerator = x
• Denominator = y

According to the 1st condition :-

• The denominator of the rational number is greater than its numerator by 8.

$\to\sf{y=x+8...............(i)}$

According to the 2nd condition :-

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

$\to\sf{\dfrac{x+17}{y-1}=\dfrac{3}{2}}$

• Put y = x+8 from eq(i).

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

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

$\to\sf{3x+21=2x+34}$

$\to\sf{3x-2x=34-21}$

$\to\sf{x=13}$

• Numerator = 13

Now put x = 13 in eq(i).

$\to\sf{y=x+8}$

$\to\sf{y=13+8}$

$\to\sf{y=21}$

• Denominator = 21

Therefore,

${\boxed{\sf{The\: rational\: number=\dfrac{13}{21}}}}$

Answer 2

Answer:

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.

Find

• What is the rational number.

According to the given question:

• Let x and y be numerator and denominator.

Equation formed case 1:

⇢ y = x + 8 --------- (1)

Equation formed case 2:

⇢ x + 17/y - 1 = 3/2

⇢ x + 17/(x + 8 - 1) = 3/2

We know that (8 - 1 = 7):

⇢ x + 17/7 = 3/2

⇢ 3x + 21 = 2x + 34

⇢ 3x - 2x = 34 - 21

⇢ x = 13 ---------- (2)

Therefore, 13 is the numerator.

Adding values from eq(2) to eq(1):

⇢ y = x + 8

⇢ y = 13 + 8

⇢ y = 21 --------- (3)

Therefore, 21 is the denominator.

Therefore, the required frictional rational number is 13/21.