If the numerator of a fraction is increased by 20% and its denominator by 25%,…
2019
If the numerator of a fraction is increased by 20% and its denominator by 25%, the resulting fraction is 3/5. What is the original fraction?
- A.
3/8
- B.
8/5
- C.
5/8
- D.
8/3
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
If x/y is a fraction and its numerator and denominator are increased by p% and q%, respectively, the new fraction is [x(1+p/100)]/[y(1+q/100)].
Therefore, the original fraction equals the new fraction multiplied by the denominator growth factor and divided by the numerator growth factor.
Application
Let the original fraction be x/y.
After the increases, the new fraction is (1.20x)/(1.25y) = 3/5.
Rearranging gives x/y = (3/5) × (1.25/1.20).
Simplify: x/y = (3/5) × (125/120) = (3/5) × (25/24) = 75/120 = 5/8.
Cross-check
Using 5/8, a 20% increase changes the numerator 5 to 6, and a 25% increase changes the denominator 8 to 10. Thus the modified fraction is 6/10 = 3/5, matching the condition.
Hence, the original fraction is 5/8.