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

Answer:

the answer of the given question is numerator =10and denominator =6

Answer 2

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.