Question

The denominator of a rational number is greater than its numerator by 5. If the numerator is increased by 8 and the denominator is decreased by 1, the new number becomes 5/3 . Find the Original number. ​

Answer 1

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf y=x+5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+8}{y-1} = \dfrac{5}{3} \\\\\longrightarrow 3(x+8) = 5 (y-1) \\\\\longrightarrow 3x+24 = 5y-5 \\\\\longrightarrow 3x-5y =- 29 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf 3x-5(x+5) = -29 \\\\\longrightarrow 3x-5x-25 = -29 \\\\\longrightarrow 3x-5x = -4 \\\\\longrightarrow -2x=-4 \\\\\longrightarrow \bf x = 2$

Substitute x = 2 in eq (1) :-

$\longrightarrow \sf y = 2+5 \\\\\longrightarrow \bf y = 7$

$\bf FRACTION = \dfrac{2}{7}$

Answer 2

$\huge{\boxed{\red{\bf{Answer:-}}}}$

GiveN:

• Denominator is greater than its numerator by 5.
• If the numerator is increased by 8 and the denominator is decreased by 1, the number becomes 5/3.

To FinD:

• The original number?

Step-by-step Explanation:

Let the numerator be x and denominator be y.

According to question,

⇒ Denominator = Numerator + 5

⇒ y = x + 5

⇒ x - y = -5

And, It is also given that:

When,

• Numerator increased by 8 = x + 8
• Denominator decreased by 1 = y - 1
• The Fraction becomes 5/3

Then,

$\rm{ \dfrac{x + 8}{y - 1} = \dfrac{5}{3} }$

Cross multiplying,

3(x+8)=5(y−1)

Expanding the parentheses,

3x+24=5y−5

3x−5y=−5−24

3x−5y=−29−−−−−(2)

Multiplying 3 with eq. (1),

⇒ 3(x - y) = -15

⇒ 3x - 3y = -15

Subtracting eq. (1) from eq. (2),

⇒ 3x - 3y - (3x - 5y) = -15 + 29

⇒ 3x - 3y - 3x + 5y = 14

⇒ 2y = 14

⇒ y = 7

Then,

⇒ x - 7 = -5

⇒ x = 2

Thus,

The original number is:

$\Large{ \boxed{ \sf{ \orange{ \dfrac{2}{7} }}}}$

Note:

After finding the answer, always recheck or verify by comparing with the conditions given.