Question

If the numerator of a fraction is increased by 200% and the denominator is increased by 200%, then resultant fraction is \(2\frac{4}{5}\). What is the original fraction?

• A. \(\frac{4}{7}\)
• B. \(\frac{13}{12}\)
• C. \(\frac{11}{12}\)
• D. None

Answer 1

The Correct Option is D

The problem involves manipulating fractions by increasing their numerator and denominator. Let the original fraction be \(\frac{a}{b}\).

Step 1: Increase both the numerator and the denominator by 200%. This means:

New Numerator = \(a + 200\%\) of \(a = a + 2a = 3a\).

New Denominator = \(b + 200\%\) of \(b = b + 2b = 3b\).

Step 2: The new fraction is given as \(2\frac{4}{5}\), which can be converted to an improper fraction:

\(2\frac{4}{5} = \frac{14}{5}\).

So, the equation becomes:

\(\frac{3a}{3b} = \frac{14}{5}\).

Simplifying the left-hand side:

\(\frac{a}{b} = \frac{14}{5}\).

This implies that the original fraction \(\frac{a}{b} = \frac{14}{5}\).

Step 3: Compare the given options for the original fraction:

Option	Value
\(\frac{4}{7}\)	\(0.571\ldots\)
\(\frac{13}{12}\)	\(1.083\ldots\)
\(\frac{11}{12}\)	\(0.916\ldots\)
None	Not matching any above

The correct original fraction, \(\frac{14}{5}\), is not any of the provided options. Therefore, the answer is 'None'.