Algebra Puzzle – Challenge 49

Challenge:

John wants to clean his house during this week. He cleaned \(\frac{1}{5}\) of his house on Sunday and \(\frac{1}{4}\) of the remaining on Monday. On Tuesday, John cleaned \( \frac{1}{3}\) of what still remained and \(\frac{1}{2}\) of what left on Wednesday. What fraction of the house needs to be cleaned?

A- \(\frac{1}{5}\)

B- \(\frac{1}{6}\)

C- \(\frac{1}{12}\)

D- \(\frac{1}{16}\)

E- \(\frac{1}{24}\)

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John cleaned \(\frac{1}{5}\) of his house on Sunday and \(\frac{1}{4}\) of the remaining on Monday.
The remaining on Monday was \(\frac{4}{5}\). Therefore, \(\frac{1}{4}\) of \(\frac{4}{5}\) equals:
\(\frac{1}{4} × \frac{4}{5} = \frac{4}{20} = \frac{1}{5}\). So, he cleaned \(\frac{1}{5}\) of his house on Sunday and another \(\frac{1}{5}\) of his house on Monday. The remaining for the next day is \(\frac{3}{5}\) of the house.
On Tuesday, John cleaned \(\frac{1}{3}\) of what still remained. \(\frac{1}{3}\) of \(\frac{3}{5}\) of the house equals:
\(\frac{1}{3} × \frac{3}{5} = \frac{3}{15} = \frac{1}{5}\). So far, he has cleaned \(\frac{3}{5}\) of the house and \(\frac{2}{5}\) of the house is left.
He cleaned \(\frac{1}{2}\) of what left (\(\frac{2}{5}\) of the house) on Wednesday. \(\frac{1}{2}\) of \(\frac{2}{5}\) of the house equals:
\(\frac{1}{2} × \frac{2}{5} =\frac{2}{10} = \frac{1}{5}\).
Therefore, \(\frac{1}{2}\) of the house needs to be cleaned.