Question

The denominator of a rational number
is greater than its numerator by 2. If the numerator is decreased by 3 and the denominator is increased by 4, the new rational number obtained is 2/5 number Find the rational number
​

Answer 1

Step-by-step explanation:

Solution :

Let,

• Numerator = x
• Denominator = x + 2

• If the numerator is decreased by 3 = x - 3

• If the denominator increased by 4 = x + 2 + 4

= x + 6

★ According to the Question :

The new rational number obtained is 2/5

$\dfrac{x \: - \: 3}{x \: + \: 6} \: = \: \dfrac{2}{5}$

⇒ 2 (x + 6) = 5 (x - 3)

⇒ 2x + 12 = 5x - 15

⇒ 12 + 15 = 5x - 2x

⇒ 27 = 3x

⇒ 27/3 = x

⇒ x = 9

Numerator = 9

• Denominator = x + 2

⇒ 9 + 2 = 11

Denominator = 11

The rational number = $\dfrac{9}{11}$

Therefore,

The rational number is $\dfrac{9}{11}$

Answer 2

Answer:

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