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
- 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?
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?
- 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?
Important Questions from Work Efficiency
Sumi can complete a job working 5 hours per day in 2 days. If she doubles her working hours per day, then in how many days will she complete the work?
Five men and 2 boys can do in 30 days as much work as 7 men and 10 boys can do in 15 days. How many boys should join 40 men to do the same work in 4 days?
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?
3 men working 7 hours a day can complete a piece of work in 45 days. In how many days will 9 men working 6 hours a day complete the same work?
