1. A can do a piece of work in 40 days, B in 30 days & (A + B + C) in 10 days. In how many days C alone can do it.
Sol:
∴ Cₑբբ = 12 – 3 + 4 = 5
∴ t꜀ to complete job alone = \(\frac{{120}}{{{C_{eff}}}}\) = \(\frac{{120}}{5}\) = 24 days Answer
2. (A+B) can do a work is 6 days, while (B+C) can do the same work in 8 days. In (C+A) can do the same work in 12 days. In how many days A, B, C together complete the whole work also find their individiual completion time.
Sol:
∴ 2(A + B + C)ₑբբ = 24 + 18 + 12
(A + B + C)ₑբբ = 27 ⟹ time to complete work = \(\frac{{144}}{{27}}\) days Answer
Aₑբբ = 27 – 18 = 9 ⟹ time to complete work = \(\frac{{144}}{9}\) = 16 days Answer
Bₑբբ = 27 – 12 = 9 ⟹ time to complete work = \(\frac{{144}}{15}\) = 9.6 days Answer
Cₑբբ = 27 – 14 = 3 ⟹ time to complete work = \(\frac{{144}}{3}\) days = 48 days Answer
3. A takes 9 days to finish a job while B takes 27 days to finish the same job. Find the ratio of their efficiencies ?
Sol:
4. A is thrice as efficient as B and A takes 40 days to do a job, then in how many days B can finish the same job.
Sol:
5. A is thrice as efficient as B and therefore able to finish a job in 100 days less than B. Find the time in which A and B can complete the work individually & in how many days they can complete the work , working together ?
Sol:
6. A can do a piece of work in 20 days. B is 25% more efficient than A. Find the number of days taken by B to do the same piece of work.
Sol:
7. A can complete a work in 10 days, B in 12 days and C in 15 days. All they began the work together but A had to leave the work after 2 days of starting & B leaves 3 days before the completion of the work. How long did the work last ?
Sol:
∴ \({t_{B + C}} = \frac{{18}}{{5 + 4}}\) = 2 days
∴ total time = 2 + 2 + 3 = 7 days Answer
Method(2):
Total time = \(\frac{{60 – 2 \times 6 + 5 \times 3}}{{5 + 4}}\)
= 7 days Answer
8. A can finish a work in 15 days and B can do it in 60 days. After A had worked for 5 days, B also joined A to finish the remaining work. Remaining work will be finished in how many days.
Sol:
time required to finish Remaining work = \(\frac{{40}}{{4 + 1}}\)
= 8 days Answer
9. A can do a piece of work in 15 days. He started the work & left after some days when 20% work was done. After it B joined and completed the work in 20 days. In how many days A & B can complete the whole work.
Sol:
∴ 80% work is done by B in 20 days
\(\frac{{20}}{{80\% }} \times 100\% \) = 25 days Time to complete work for B
10. A alone can complete a work in 14 days and B alone in 18 days. Starting with A they work on alternate days. The total work will be completed in how many days.
Sol:
Now A wil come & do 9 work in 1 day so till now 14 + 1 = 15 days have passed
Now B will come & do remaining work (6) in \(\frac{6}{7}\) days.
∴ total number of days to complete work = 15 + \(\frac{6}{7}\)
= \(15\frac{6}{7}\) days Answer