Question

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

Answer 1

Answer:

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Step-by-step explanation:

Let the numerator of a rational number = x

Then the denominator of a rational number = x + 3

When numerator is increased by 7, then new numerator = x + 7

When denominator is decreased by 1, then new denominator = x + 3 - 1

The new number formed = 3/2

According to the question,

(x + 7)/(x + 3 - 1) = 3/2

⇒ (x + 7)/(x + 2) = 3/2

⇒ 2(x + 7) = 3(x + 2)

⇒ 2x + 14 = 3x + 6

⇒ 3x - 2x = 14 - 6

⇒ x = 8

The original number i.e., x/(x + 3) = 8/(8 + 3) = 8/11

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Answer 2

Answer:

Step-by-step explanation:

let numerator be x  

the denominator will be x+8

x+17/x+8-1=3/2

x+17/x+7=3/2

2(x+17)=3(x+7)

2x+34=3x+21

34-21=3x-2x  

13=x

x/x+8

13/21     (Ans  )