Question:
4 men can do a work in 5 days and 5 women can do it in 6 days. How many women should work with 2 men to complete the work in 5 days?
4 men can do a work in 5 days and 5 women can do it in 6 days. How many women should work with 2 men to complete the work in 5 days?
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Work = Efficiency × Time
Updated On: Apr 21, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Find 1 man's 1-day work.
4 men complete work in 5 days.
1 man's 1-day work = \(\frac{1}{4 \times 5} = \frac{1}{20}\). Step 2: Find 1 woman's 1-day work.
5 women complete work in 6 days.
1 woman's 1-day work = \(\frac{1}{5 \times 6} = \frac{1}{30}\). Step 3: Define number of women needed = \(w\).
Work done in 5 days by 2 men and \(w\) women = 1 (whole work).
\(5 \times \left( \frac{2}{20} + \frac{w}{30} \right) = 1\). Step 4: Simplify the equation.
\(\frac{2}{20} + \frac{w}{30} = \frac{1}{5}\).
\(\frac{1}{10} + \frac{w}{30} = \frac{1}{5}\). Step 5: Solve for \(w\).
\(\frac{w}{30} = \frac{1}{5} - \frac{1}{10} = \frac{2}{10} - \frac{1}{10} = \frac{1}{10}\).
\(w = 30 \times \frac{1}{10} = 3\).
4 men complete work in 5 days.
1 man's 1-day work = \(\frac{1}{4 \times 5} = \frac{1}{20}\). Step 2: Find 1 woman's 1-day work.
5 women complete work in 6 days.
1 woman's 1-day work = \(\frac{1}{5 \times 6} = \frac{1}{30}\). Step 3: Define number of women needed = \(w\).
Work done in 5 days by 2 men and \(w\) women = 1 (whole work).
\(5 \times \left( \frac{2}{20} + \frac{w}{30} \right) = 1\). Step 4: Simplify the equation.
\(\frac{2}{20} + \frac{w}{30} = \frac{1}{5}\).
\(\frac{1}{10} + \frac{w}{30} = \frac{1}{5}\). Step 5: Solve for \(w\).
\(\frac{w}{30} = \frac{1}{5} - \frac{1}{10} = \frac{2}{10} - \frac{1}{10} = \frac{1}{10}\).
\(w = 30 \times \frac{1}{10} = 3\).
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