Question

The numerator of fraction is 1 less than its denominator . If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5 .What is the original fraction ?​

Answer 1

Answer:

The original fraction is 4/5.

Explanation:

Given :-

• The numerator of fraction is 1 less than its denominator.
• If the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4/5.

To find :-

• The original fraction.

Solution :-

Consider,

• Denominator of the fraction = x

★ The numerator of fraction is 1 less than its denominator.

Then,

• Numerator of the fraction = (x-1)

★If the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4/5.

• Numerator = (x-1+4) = (x+3)
• Denominator = (x+5)

According to the question,

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

→ 5x +15 = 4x +20

→ 5x-4x = 20-15

→ x = 5

Then,

• Denominator = 5
• Numerator = (5-1) = 4

Therefore,

${\boxed{\sf{Original\: fraction=\dfrac{4}{5}}}}$

Answer 2

Explanation:

Given :-

• The numerator of fraction is 1 less than its denominator.

•If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5.

To Find :-

• What's the original fraction?

Solution :-

Let the numerator and denominator of the fraction be x and y respectively.

As per question :-

Given that,

The numerator of fraction is 1 less than its denominator.

Therefore,

x = y−1................eq(1)

Again, it’s given that

If the numerator is increased by 4 and the denominator is increased by 5 the new fraction becomes equivalent to 4/5.

Therefore,

(x + 4) / ( y + 5) = 4/5

⟼ 5x +20 = 4y +20

⟼ 5x - 4y = 0........eq(2)

Substitute x = y - 1 in eq(2)

5x - 4y = 0

⟼ 5 ( y -1) - 4y =0

⟼ 5y - 5 - 4y = 0

⟼ y = 5

Now, put the value of y in eq(1)

x = y -1

⟼ x = 5 - 1

⟼x = 4⟼x=4

Hence, denominator of the fraction is = 5

Numerator of the fraction is = 4

We know,

Fraction = Numerator / Denominator

Therefore,

original fraction is = 4/5