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The numerator of a number is smaller than its denominator by 5. If the numerator is increased by 8 and denominator by 6, then the new number becomes 5/7. Find the rational number.

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The numerator of a number is smaller than its denominator by 5. If the numerator is increased by 8 and denominator by 6, then the new number becomes 5/7. Find the rational number.
1). -4/3
2). 4/3
3). 1/2
4). -1/9


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1 answers

2 vote
Answered by on | Votes 2 |

Let the denominator of rational number be x.

Numerator = (x - 5)

New denominator = (x + 6)

New numerator = (x - 5 + 8) = (x + 3)

Given that, (x + 3)/ (x + 6) = 5/7

⇒ 7x + 21 = 5x + 30

⇒ 2x = 9

⇒ x = 9/2

Original rational number = (x - 5)/x = -(1/2)/(9/2) = -1/9

∴ Answer is -1/9

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