A rational number has its denominator greater than its numerator by 6.

1.	A rational number has its denominator greater than its numerator by 6. If the numerator is increased by 4 and the denominator is decreased by 8, the number becomes 5/3. What is the original rational number ?1. 11/172. 5/173. 7/134. 13/19
Answer» Correct Answer - Option 1 : 11/17 Concept used: The numerator is the upper part and denominator is the lower part of any fraction Calculation: Let the numerator of the rational number be x then its denominator be x + 6 Rational number = Numerator/Denominator The original rational number = x/(x + 6) Now, A/Q (x + 4)/(x + 6 – 8) = 5/3 ⇒ (x + 4)/(x – 2) = 5/3 ⇒ 3(x + 4) = 5(x – 2) ⇒ 3x + 12 = 5x – 10 ⇒ 2x = 22 ⇒ x = 11 Numerator = x and Denominator = 11 + 6 = 17 ∴ The original rational number is 11/17

A rational number has its denominator greater than its numerator by 6. If the numerator is increased by 4 and the denominator is decreased by 8, the number becomes 5/3. What is the original rational number ?1. 11/172. 5/173. 7/134. 13/19

Answer» Correct Answer - Option 1 : 11/17

Concept used:

The numerator is the upper part and denominator is the lower part of any fraction

Calculation:

Let the numerator of the rational number be x then its denominator be x + 6

Rational number = Numerator/Denominator

The original rational number = x/(x + 6)

Now, A/Q

(x + 4)/(x + 6 – 8) = 5/3

⇒ (x + 4)/(x – 2) = 5/3

⇒ 3(x + 4) = 5(x – 2)

⇒ 3x + 12 = 5x – 10

⇒ 2x = 22

⇒ x = 11

Numerator = x and Denominator = 11 + 6 = 17

∴ The original rational number is 11/17

Discussion

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