Question

2.
The denominator of a rational number is greater than its numerator by 3. If the numerator
isincreased by 7 and the denominator is decreased by 1. the new number becomes 3/2. The
original number
​

Answer 1

~AЙSWEЯ.

⇒ Let us take the numerator as '$x$'

⇒ The denominator will be '$x + 3$'

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⇒ $\frac{x+7}{x+3-1} = \frac{3}{2}$

⇒ $\frac{x+7}{x+2} = \frac{3}{2}$

⇒ $2(x+7) = 3( x + 2)$

⇒ $2x + 14 = 3x + 6$

⇒ $14 - 6 = 3x-2x$

⇒ $\fbox{8 = x}$

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So, the original number is : $\frac{8}{11}$

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Thanks

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Answer 2

Answer:

Original number is 8 / 11

Step-by-step explanation:

Given :

• The denominator of a rational number is greater than its numerator by 3

• Numerator is increased by 7

• The denominator is decreased by 1

• The new number becomes 3/2

Find :

• Original rational number

Solution :

Let,

The numerator of rational number = x

The denominator of rational number = x + 3

The numerator is increased by 7

The denominator is decreased by 1

So,

The numerator of new rational no. = x + 7

The denominator of new rational no. = x + 3 - 1

⇒ (x + 3) - 1

⇒ x + 3 - 1 = x + 2

⇒ x + 2

The new number becomes 3/2

⇒ x + 7 /x +2 = 3/2

⇒ 2 (x+7) = 3 (x+2)

⇒ 2x + 14 = 3x + 6

⇒ 2x - 3x = 6 - 14

⇒ -1x = - 8

⇒ x = 8

Numerator of rational number is 8

Denominator of rational number is = x + 3

⇒ x + 3

⇒ 8 + 3

⇒ 11

Therefore,

Original number is 8 / 11