If the numerator of a fraction is increased by 200% and the denominator is increased by 400%, the resultant fraction is \(1\frac{1}{20}\). What was the original fraction?

Given:

The numerator is increased by 200%.

The denominator is increased by 400%.

Formula Used:

Original fraction = numerator/denominator

Calculation:

Let the original fraction be x/y.

Numerator after increase = x × (1 + 200%) = x × (1 + 2) = 3x

Denominator after increase = y × (1 + 400%) = y × (1 + 4) = 5y

Resultant fraction = 1(1)/(20) = 21/20

Given, (3x) / (5y) = 21 / 20

Cross-multiply to solve for x/y:

⇒ 3x × 20 = 21 × 5y

⇒ 60x = 105y

⇒ x / y = 105 / 60

⇒ x / y = 7 / 4

Hence, the original fraction is 7/4 = \(1\frac{3}{4}\)

The original fraction is \(1\frac{3}{4}\).