Two men and three boys can do a piece of work in ten days; while three men and two boys can do the same work in eight days. In how many days can two men and one boy do the work?
1. Set Up the Work Equations - Let 'm' be the amount of work one man does per day, and 'b' be the work one boy does per day.
- The total work done is the same in both scenarios. We can express this as: Total Work = Rate × Time.
- Scenario 1: Total Work = (2m + 3b) × 10 days.
- Scenario 2: Total Work = (3m + 2b) × 8 days.
2. Find the Relationship Between Man and Boy Rates - Since the total work is equal, we can set the two equations equal to each other:
- 10(2m + 3b) = 8(3m + 2b)
- 20m + 30b = 24m + 16b
- 14b = 4m
- This gives us the relationship: m = (7/2)b. (This means one man works as fast as 3.5 boys).
3. Calculate the Total Work - Now, substitute the relationship back into the first equation to find the total work in terms of a single unit (like 'boy-days'):
- Total Work = (2(7/2)b + 3b) × 10 = (7b + 3b) × 10 = 10b × 10 = 100b.
4. Calculate Time for the New Group - The new group is 2 men and 1 boy. Let's find their combined rate in terms of 'b':
- New Rate = 2m + 1b = 2(7/2)b + 1b = 7b + 1b = 8b.
- The time required is Total Work divided by the New Rate:
- Time = 100b / 8b = 12.5 days.
Final Answer: It will take the new group 12.5 days to complete the work.
Reinforce your conceptual grasp with related questions from NIMCET 2018:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →