Question

PAGE NO. DATE: The numerator of a fraction is 2 less than the denominator. If 3 is added to both the fraction become 3/4. Find the fraction​

Answer 1

Answer:

The fraction is $\dfrac{3}{5}$

Step-by-step explanation:

Let,

• The numerator of a fraction = x
• The denominator of a fraction = x + 2

If 3 is added to both

• The numerator of a fraction = x + 3

• The denominator of a fraction = x + 2 + 3

$\longrightarrow$ x + 5

• The fraction become 3/4.

★ According to the Question :

$\longrightarrow \: \dfrac{(x \: + \: 3)}{(x \: + \: 5)} \: = \: \dfrac{3}{4}$

$\longrightarrow$ 4 (x + 3) = 3 (x + 5)

$\longrightarrow$ 4x + 12 = 3x + 15

$\longrightarrow$ 4x - 3x = 15 - 12

$\longrightarrow$ x = 3

The numerator of a fraction = 3

• The denominator of a fraction = x + 2

$\longrightarrow$ 3 + 2

$\longrightarrow$ 5

The denominator of a fraction = 5

∴ The fraction is $\dfrac{3}{5}$

Answer 2

Step-by-step explanation:

• Condition 1 -

The numerator of a fraction is 2 less than the denominator.

• Condition 2 -

3 is added to both the fraction become 3/4

Consider the following as,

In original fraction -

• Numerator = n
• Denominator = d

As per condition 1, Numerator will be (d - 2).

➨ n = (d - 2) ----- (equation I)

Original fraction becomes = (d - 2)/d

Following condition 2,

• Numerator = n + 3
• Denominator = d + 3

Fraction becomes = (n + 3)/(d + 3)

Put equation I in the new fraction,

➨ [(d - 2) + 3]/(d + 3)

➨ (d + 1)/(d + 3) ---- (II)

According the the second condition, new fraction becomes 3/4

Equate II and 3/4

➨ (d + 1)/(d + 3) = 3/4

➨ 4(d + 1) = 3(d + 3)

➨ 4d + 4 = 3d + 9

➨ 4d - 3d = 9 - 4

➨ d = 5

Place value of d in original fraction,

➨ (d - 2)/d

➨ (5 - 2)/5

➨ 3/5

Hence, the original fraction is 3/5.