Question : A and B can do a work in $26 \frac{2}{3}$ days. B and C together can complete the same work in 48 days, while A and C together can complete the same work in 30 days. How long (in days) will A alone take to complete 60% of the work?
Option 1: 20
Option 2: 32
Option 3: 24
Option 4: 36
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Correct Answer: 24
Solution : Use : Work = Efficiency × Time According to the question LCM of $\frac{80}{3}$, 48 and 30 = 720 ⇒ Efficiency of A and B = 720 × $\frac{3}{80}$ = 27 ⇒ Efficiency of B and C = $\frac{720}{48}$ = 15 ⇒ Efficiency of A and C = $\frac{720}{30}$ = 24 Total Time Taken by A, B, and C to Complete Work = $\frac{27+15+24}{2}=\frac{64}{2}= 32$ days Now, Time Taken by A, B, and C to complete the 60 % of the work = $\frac{\text{60% of the total work}}{\text{Time}}$ = $\frac{720}{33 – 15}$ × $\frac{60}{100}$ = $\frac{720}{18}$ × $\frac{3}{5}$ = $24$ days Hence, the correct answer is 24.
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Question : A, B and C together can complete a work in 12 days. A and B alone can do the same work in 36 days. In how many days can C alone complete the same work?
Option 1: 48
Option 2: 25
Option 3: 12
Question : A can do $\frac{1}{3}$rd of a piece of work in 32 days, B can do $37 \frac{1}{2}$% of the same work in 24 days, while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left and A joined C and together, completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 : 11, then what fraction of the same work can be completed by C alone in 3.5x days?
Option 1: $\frac{18}{25}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{7}{10}$
Option 4: $\frac{3}{4}$
Question : Ganesh, Ram, and Sohan can complete a work in 16 days. If Ganesh and Ram together can complete the same work in 24 days, the number of days Sohan alone takes to finish the work is:
Option 1: 40
Option 2: 48
Option 3: 32
Option 4: 30
Question : A can do $\frac{1}{3}$ of a work in 30 days. B can do $\frac{2}{5}$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:
Option 1: 15 days
Option 2: 10 days
Option 3: 18 days
Option 4: 12 days
Question : A and B together can do a piece of work in 12 days. A alone can do it in 18 days. In how many days B alone can do the work?
Option 1: 36 days
Option 2: 24 days
Option 3: 32 days
Option 4: 30 days
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