The denominator of a fraction is 2 more than numerator. If the numerator as…
2023
The denominator of a fraction is 2 more than numerator. If the numerator as well as denominator is increased by 4, the fraction becomes 8/10. Find the original fraction.
- A.
2/3
- B.
2/9
- C.
7/9
- D.
9/8
Show answer & explanation
Correct answer: A
Concept: For a word problem describing a fraction whose numerator and denominator are related, and which becomes a known value after a common addition, use ONE variable for the numerator, express the denominator in terms of it from the given relationship, form an equation for the fraction after the addition, and solve by cross-multiplication.
Application: Let the numerator be x. Since the denominator is 2 more than the numerator, the denominator is x + 2.
Adding 4 to both numerator and denominator gives the new fraction (x + 4)/(x + 6).
This new fraction equals 8/10, so (x + 4)/(x + 6) = 8/10.
Cross-multiplying: 10(x + 4) = 8(x + 6).
Expanding: 10x + 40 = 8x + 48.
Simplifying: 2x = 8, so x = 4.
Denominator = x + 2 = 6, so the original fraction is 4/6, which reduces to 2/3.
Cross-check: Denominator − numerator = 6 − 4 = 2, satisfying the first condition. Adding 4 to each: (4+4)/(6+4) = 8/10, satisfying the second condition. Both conditions hold, confirming the answer.
Answer: The original fraction is 2/3.
