# Algebra Puzzle – Challenge 49

A great math brain teaser and puzzle for smart ones! Try this math challenge to boost your brainpower with scientific exercises!

## 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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The correct answer is A.

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.

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