Question

the numerator of a fraction is 5 less than its denominator.
if 3 is added to its numerator and denominator both, the fraction becomes 4/5
find the original fraction.​​

Answer 1

Answer:

17/22

Step-by-step explanation:

Assume that the numerator be N and denominator be D.

So, the original fraction is N/D.

Given that, the numerator of a fraction is 5 less than its denominator.

→ N = D - 5 --------- (1)

Also given that, if 3 is added to its numerator and denominator both, the fraction becomes 4/5.

→ (N + 3)/(D + 3) = 4/5

→ 5(N + 3) = 4(D + 3)

→ 5N + 15 = 4D + 12

→ 5N - 4D = 12 - 15

→ 5(D - 5) - 4D = -3

→ 5D - 25 - 4D = - 3

→ D = -3 + 25

→ D = 22

Now, substitute the value of D in (1)

→ N = 22 - 5

→ N = 17

Now, fraction = N/D = 17/22.

Hence, the original fraction is 17/22.

Answer 2

Step-by-step explanation:

Solution :

Let,

• Numerator = x
• Denominator = x + 5

If 3 is added to its numerator and denominator both, the fraction becomes 4/5

• Numerator = x + 3
• Denominator = x + 5 + 3 = x + 8

★ According to the Question :

$\dfrac{x + 3}{x + 8} = \dfrac{4}{5}$

5 (x + 3) = 4 (x + 8)

5x + 15 = 4x + 32

5x - 4x = 32 - 15

x = 17

Numerator = 17

• Denominator = x + 5

17 + 5

22

The original fraction = 17/22

Therefore, The original fraction is 17/22.