6 days
Efficiency Ratio Interpretation
The efficiency ratio of A, B, and C is given as $2:3:5$. This implies that their rates of work are in this proportion.
Let the amount of work done per day by A, B, and C be $2x$, $3x$, and $5x$ units respectively. Here, $x$ represents a common factor.
Calculating Total Work
We know that A alone can complete the work in 40 days.
- Work done by A per day = $2x$ units.
- Total work = (Work rate of A) $\times$ (Time taken by A)
- Total work = $2x \times 40 = 80x$ units.
Work Done Together
A, B, and C worked together for 5 days.
- Combined work rate of A, B, and C = $2x + 3x + 5x = 10x$ units per day.
- Work done in 5 days = (Combined work rate) $\times$ (Time)
- Work done in 5 days = $10x \times 5 = 50x$ units.
Calculating Remaining Work
After 5 days, the remaining work is calculated as:
- Remaining Work = Total Work - Work done in 5 days
- Remaining Work = $80x - 50x = 30x$ units.
Time for A and B to Complete Remaining Work
C left the work, and A and B together completed the remaining work.
- Combined work rate of A and B = $2x + 3x = 5x$ units per day.
- Number of days required = $\frac{\text{Remaining Work}}{\text{Combined work rate of A and B}}$
- Number of days required = $\frac{30x}{5x} = 6$ days.
Similar Questions
- A can complete a task in $30\text{ days}$, and B can complete the same task in $40\text{ days}$. They work together for $10\text{ days}$, and then C joins them and completes the remaining work in $5\text{ days}$. How long will C alone take to complete the task?
A and B can complete a task in 12 days together. A is 25% more efficient than B. What percentage of the work is done by A alone?
20 women can do work in 16 days. 10 men can complete the same work in 12 days. What is the ratio between the efficiency of a man and a woman?
- Sameer can complete a work in 16 days. In how many days will the work be completed by Ajay, if his efficiency is 60% more than that of Sameer?
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?
