If numerator of a fraction is increased by 25% and the denominator is…
2023
If numerator of a fraction is increased by 25% and the denominator is decreased by 15%, the fraction becomes 15/17. Find the value of the original fraction.
Answer: A. 3/5 — ConceptWhen the numerator of a fraction is multiplied by a factor p and its denominator by a factor q, the fraction itself is multiplied by p/q. Convert each…
- A.
3/5
- B.
4/5
- C.
7/5
- D.
6/5
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept
When the numerator of a fraction is multiplied by a factor p and its denominator by a factor q, the fraction itself is multiplied by p/q. Convert each percentage change into a multiplicative factor before forming an equation.
Application
Let the original fraction be x.
A 25% increase multiplies the numerator by 5/4, and a 15% decrease multiplies the denominator by 17/20.
Therefore the new fraction is x × (5/4) ÷ (17/20) = x × 25/17.
Using the given value, x × 25/17 = 15/17.
Solving gives x = (15/17) × (17/25) = 15/25 = 3/5.
Cross-check
For 3/5, the changed fraction is (3 × 5/4) ÷ (5 × 17/20) = (15/4) ÷ (17/4) = 15/17, which matches the stated changed fraction. Hence the original fraction is 3/5.