Correct Answer - Option 4 : 272/1495
Given:
If the numerator of a fraction is increased by 15% and the denominator is decreased by 20%, then the fraction becomes 17/85.
Calculation:
Let the numerator of the fraction be N, and the denominator of the fraction be D.
New numerator = N + (15/100) × N
⇒ (100N + 15N)/100
⇒ 115N/100
New denominator = D – (20/100) × D
⇒ (100D – 20D)/100
⇒ 80D/100
New fraction = 115N/80D
⇒ (17/65) = (23N/16D)
⇒ 17 × 16D = 23N × 65
⇒ 272D = 1495N
⇒ N/D = 272/1495
∴ The original fraction is 272/1495.
