Question : A and B can complete a piece of work in 13 and 17 days respectively. A begins to do the work, and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $17 \frac{11}{17}$ days
Option 2: $17 \frac{17}{19}$ days
Option 3: $14 \frac{11}{17}$ days
Option 4: $11 \frac{11}{17}$ days
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Correct Answer: $14 \frac{11}{17}$ days
Solution : Time taken by A to complete the work = 13 days Part of work done by A alone in a day = $\frac{1}{13}$ Time taken by B to complete the work = 17 days Part of work done by B alone in a day = $\frac{1}{17}$ Work done by A and B in the first 2 days if they work alternatively = $\frac{1}{13}$ + $\frac{1}{17}$ = $\frac{13+17}{13×17}$ = $\frac{30}{221}$ Work done by A and B in 14 days = $\frac{7×30}{221}$ = $\frac{210}{221}$ Remaining work = $1-\frac{210}{221}=\frac{221-210}{221}$ = $\frac{11}{221}$ So, the time taken by A to complete the rest = $\frac{\frac{11}{221}}{\frac{1}{13}}$ = $\frac{11}{17}$ Thus, the total time taken by A and B to complete the work when they work alternatively = $14\frac{11}{17}$ days Hence, the correct answer is $14\frac{11}{17}$ days.
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Question : A and B can complete a work in 10 and 16 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in:
Option 1: $12 \frac{1}{4}$ days
Option 2: $13 \frac{1}{4}$ days
Option 3: $15 \frac{1}{4}$ days
Option 4: $14 \frac{1}{4}$ days
Question : X and Y can complete a work in 9 days and 36 days, respectively. X begins to do the work and they work alternately one at a time for one day each. The whole work will be completed in:
Option 1: $12\frac{1}{2}$ days
Option 2: $14\frac{1}{4}$ days
Option 3: $13\frac{1}{3}$ days
Option 4: $15\frac{1}{5}$ days
Question : A, B, and C working alone, can complete a job in 16, 24, and 36 days, respectively. In how many days can they complete the job if they work together?
Option 1: $7 \frac{11}{19}$
Option 2: $5 \frac{17}{19}$
Option 3: $4 \frac{13}{19}$
Option 4: $6 \frac{7}{19}$
Question : Pawan can do a piece of work in 32 days. He worked for 8 days and left the work. Thereafter Sandeep finished the remaining work in 27 days. In how many days can Pawan and Sandeep together do the whole work?
Option 1: $16 \frac{16}{17}$ days
Option 2: $16 \frac{13}{17}$ days
Option 3: $16 \frac{15}{17}$ days
Option 4: $16 \frac{14}{17}$ days
Question : P, Q, and R can complete a piece of work in 10 days, 15 days, and 20 days, respectively. If they work together, in how many days can they finish the same work?
Option 1: $4 \frac{8}{13}$
Option 2: $4 \frac{3}{7}$
Option 3: $4 \frac{7}{13}$
Option 4: $4 \frac{5}{7}$
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