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?
- 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?
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 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
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?
