Understanding Work and Efficiency Concepts
This problem is about calculating the time taken to complete a task based on the efficiency of the individuals involved. Efficiency relates to how much work can be done in a specific amount of time. The basic formulas are:
- Efficiency = Work / Time
- Work = Efficiency × Time
- Time = Work / Efficiency
The goal is to find the number of days person A needs to finish a piece of work entirely on their own.
Analyzing the Efficiency Relationship
The core information given is:
- Person A is three times more efficient than Person B.
- Together, A and B finish the work in 30 days.
Interpreting "A is three times more efficient than B": While technically this could mean $E_A = E_B + 3E_B = 4E_B$, standard aptitude problems often use this phrasing to mean $E_A = 3 \times E_B$. Given that the likely answer is an integer (40), we will proceed using the interpretation that A's efficiency is exactly 3 times B's efficiency.
- Let $E_B$ represent the efficiency of B (amount of work B does per day).
- Let $E_A$ represent the efficiency of A (amount of work A does per day).
- Using our interpretation: $E_A = 3 \times E_B$.
Calculating the Time for A to Finish Work Alone
We can solve this step-by-step:
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Calculate Combined Efficiency:
When A and B work together, their efficiencies add up. Combined Efficiency $= E_A + E_B$ Substituting the relationship $E_A = 3E_B$: Combined Efficiency $= (3E_B) + E_B = 4E_B$. So, together they achieve an efficiency equivalent to 4 times B's individual efficiency.
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Determine the Total Work:
The total amount of work ($W$) can be found by multiplying the combined efficiency by the time they worked together (30 days). $W = \text{Combined Efficiency} \times \text{Time Taken Together}$ $W = (4E_B) \times 30 \text{ days}$ $W = 120 E_B \text{ units of work}$. This value represents the total effort required to complete the job.
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Calculate Time Taken by A Alone:
To find how many days A needs to complete the work alone ($T_A$), divide the total work by A's individual efficiency. $T_A = \frac{\text{Total Work}}{E_A}$ Using the values we found: $W = 120 E_B$ and $E_A = 3 E_B$. $T_A = \frac{120 E_B}{3 E_B}$ The term $E_B$ cancels out, leaving: $T_A = \frac{120}{3}$ $T_A = 40 \text{ days}$.
Thus, A alone can finish the same piece of work in 40 days.
Similar Questions
- If 9 men and 6 women working together can do six times as much work per hour as 1 man and 2 women working together, then the ratio of the work done by 1 man to that of 1 woman in a given time is:
If machine A and B can produce 800 units in 3 hours and 8 hours, respectively, in how many hours can machine A and B working together at these constant rates produce 800 units?
Important Questions from Work Efficiency
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
