Practice Questions
Concept Explanation
Different groups may have different efficiencies. Convert all to a common unit (man-days, woman-days).
Key Formulas
- If 2 men = 3 women in efficiency, then 1 man = 1.5 women
- Total work = Number of workers × Efficiency × Days
- Compare using equivalent man-days or woman-days
Example
2 men = 3 women. 6 men finish in 10 days. Work = 60 man-days = 90 woman-days. 9 women need 10 days.
Common Trap
Convert to equivalent workers before applying M1D1 = M2D2.
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Q1 Easy5 women can finish a work in 12 days. If 1 man can do as much work as 2 women, how many days will 3 men take to finish the same work?ExplanationTotal work = 60 woman-days = 30 man-days. Time for 3 men = 30/3 = 10 days.
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Q2 EasyIf 1 man can do as much work as 3 women, and 2 men can finish a work in 9 days, how many days will 6 women take to finish the same work?ExplanationTotal work = 18 man-days = 54 woman-days. Time for 6 women = 54/6 = 9 days.
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Q3 EasyIf 2 men can do as much work as 5 boys, and 4 men can finish a work in 10 days, how many days will 10 boys take to finish the same work?Explanation4 men and 10 boys have the same work rate. So 10 boys also take 10 days.
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Q4 MediumIf 2 men can do as much work as 3 women, how many days will 9 women take to finish the work that 6 men can finish in 10 days?ExplanationTotal work = 60 man-days = 90 woman-days. Time for 9 women = 90/9 = 10 days.
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Q5 MediumIf 1 man can do as much work as 2 boys, how many days will 8 boys take to finish the work that 5 men can finish in 6 days?ExplanationTotal work = 30 man-days = 60 boy-days. Time for 8 boys = 60/8 = 7.5 days.
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Q6 Medium4 men can finish a work in 12 days. If 1 man can do as much work as 2 women, how many days will 2 men and 4 women take to finish the same work?ExplanationTotal work = 48 man-days. 4 women = 2 men. Combined workforce = 4 man-equivalents. Time = 48/4 = 12 days.
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Q7 Medium3 men and 2 women can finish a work in 8 days. If 1 man can do as much work as 2 women, how many man-days of work are required for the work?Explanation2 women = 1 man. Total workforce = 4 man-equivalents. Work = 4 × 8 = 32 man-days.
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Q8 Medium5 boys can finish a work in 15 days. If 1 man can do as much work as 5 boys, how many days will 2 men take to finish the same work?ExplanationTotal work = 75 boy-days = 15 man-days. Time for 2 men = 15/2 = 7.5 days.
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Q9 Hard4 men and 6 women can finish a work in 6 days. If 2 men can do as much work as 3 women, how many man-days of work are required for the work?Explanation6 women are equivalent to 4 men. Total workforce = 8 man-equivalents. Work = 8 × 6 = 48 man-days.
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Q10 Hard3 men and 4 women can finish a work in 5 days. If 1 man can do as much work as 2 women, how many days will 5 men take to finish the same work alone?Explanation4 women = 2 men. Total workforce = 5 man-equivalents. Work = 25 man-days. Time for 5 men = 25/5 = 5 days.
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Q11 Hard6 men can finish a work in 10 days and 8 women can finish the same work in 15 days. How many days will 3 men and 4 women take to finish the work together?ExplanationTotal work = 60 man-days. 4 women = 2 men. Combined workforce = 5 man-equivalents. Time = 60/5 = 12 days.
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Q12 Hard2 men and 3 boys can finish a work in 10 days. If 1 man can do as much work as 3 boys, how many days will 1 man take to finish the work alone?Explanation3 boys = 1 man. Total workforce = 3 man-equivalents. Work = 30 man-days. One man alone takes 30 days.
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Q13 Hard4 men and 4 women can finish a work in 5 days. If 2 men can do as much work as 3 women, how many woman-days of work are required for the work?Explanation4 men are equivalent to 6 women. Total workforce = 10 women. Work = 10 × 5 = 50 woman-days.
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Q14 HardOne man can finish a work in 12 days and 2 boys can finish the same work in 18 days. How many days will 4 men and 6 boys take to finish the work together?ExplanationCombined rate = 4/12 + 6/36 = 1/3 + 1/6 = 1/2 per day. Time = 2 days.
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DS1 Medium
How many days will 9 women take to finish the work?
Statement I2 men can do as much work as 3 women.
Statement II6 men can finish the work in 10 days.
ExplanationTotal work = 60 man-days = 90 woman-days. Time for 9 women = 10 days. -
DS2 Medium
How many days will 8 boys take to finish the work?
Statement I1 man can do as much work as 2 boys.
Statement II5 men can finish the work in 6 days.
ExplanationTotal work = 30 man-days = 60 boy-days. Time for 8 boys = 7.5 days.
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DS3 Medium
Can 3 men finish the work in less than 10 days?
Statement I3 men and 4 women can finish the work in 5 days.
Statement II1 man can do as much work as 2 women.
ExplanationTogether: total work = 25 man-days. Three men need 25/3 ≈ 8.33 days, which is less than 10 days. -
DS4 Hard
How many man-days of work are required for the work?
Statement I4 men and 6 women can finish the work in 6 days.
Statement II2 men can do as much work as 3 women.
ExplanationBoth statements are needed: 6 women = 4 men, so total work = 8 × 6 = 48 man-days.