If the numerator of a fraction is increased by 200% and denominator is…

2023

If the numerator of a fraction is increased by 200% and denominator is increased by 250% , then the resultant fraction is 3/14. What is the original fraction ?

  1. A.

    1/2

  2. B.

    3/4

  3. C.

    1/4

  4. D.

    1/8

Attempted by 3 students.

Show answer & explanation

Correct answer: C

CONCEPT: If a quantity increases by p%, its new value equals the original value multiplied by (1 + p/100). So a p% increase corresponds to a multiplier of (100 + p)/100.

  1. Let the original fraction be x/y.

  2. The numerator is increased by 200%, so the new numerator = x × (1 + 200/100) = 3x.

  3. The denominator is increased by 250%, so the new denominator = y × (1 + 250/100) = 7y/2.

  4. So the new fraction = 3x ÷ (7y/2) = 6x/7y.

  5. The resultant fraction is given as 3/14, so 6x/7y = 3/14.

  6. Solving for x/y: x/y = (3/14) × (7/6) = 21/84 = 1/4.

Cross-check: for x/y = 1/4, the new numerator = 3 × 1 = 3 and the new denominator = 3.5 × 4 = 14, giving 3/14 — exactly the given resultant fraction, confirming the result independently.

So the original fraction is 1/4.

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