Question : A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days will the work be completed, if they both work on alternate days, starting with B?
Option 1: $5\frac{1}{3}$
Option 2: $5\frac{2}{3}$
Option 3: $5$
Option 4: $5\frac{1}{4}$
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Correct Answer: $5\frac{2}{3}$
Solution : Given: Time taken by A to complete the work = 4 days Time taken by B to complete the work = 9 days They both work on alternate days, starting with B. Let the total work = LCM of 4 and 9 = 36 units A’s 1 day's work = $\frac{36}{4}$ = 9 units B’s 1 day's work = $\frac{36}{9}$ = 4 units If they work on alternate days they will finish (4 + 9) = 13 units of work in 2 days, In 4 days they will finish (13 × 2) = 26 units of work, On the 5th day, B will finish 4 more units, So, (26 + 4) = 30 units of work is done. We have remaining (36 – 30) = 6 units of work, but A can finish 9 units in a day. So, he will able to finish 6 units in $\frac{6}{9}=\frac{2}{3}$ day itself. $\therefore$ Total work will be completed in $(5+\frac{2}{3})=5\frac{2}{3}$ days Hence, the correct answer is $5\frac{2}{3}$.
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Question : Amar can complete a work in 15 days and Prem in 12 days. Starting with Amar, they work on alternate days. In how many days will the work be completed?
Option 1: $13\frac{2}{5}$
Option 2: $12\frac{1}{6}$
Option 3: $13\frac{1}{2}$
Option 4: $13$
Question : P, Q, and R can finish a work in 5 days, 10 days, and 15 days, respectively, working alone. P and Q work on the first day, P and R work on the second day, P and Q work on the third day and so on till the work is completed. In how many days the work will be completed?
Option 1: $\frac{13}{2}$
Option 2: $\frac{9}{2}$
Option 3: $\frac{7}{2}$
Option 4: $\frac{5}{2}$
Question : A can do a task in 8 days, while B can do it in 18 days. In how many days will the work be completed if they both work on alternate days, starting with B?
Option 1: $11 \frac{1}{3}$ days
Option 2: $12 \frac{1}{3}$ days
Option 3: $10$ days
Option 4: $10 \frac{1}{3}$ days
Question : A can complete a task in 25 days while B can complete the same task in 30 days. They work on alternate days, starting with A. Both A and B follow this pattern for 5 days and then, A leaves. In how many days will B finish the remaining work?
Option 1: $24 \frac{2}{5}$
Option 2: $5 \frac{2}{5}$
Option 3: $5 \frac{3}{5}$
Option 4: $24 \frac{3}{5}$
Question : Raju, Shobh, and Mohan can do a work in 15 days, 20 days and 25 days respectively. In how many days, will the work be finished, if they do it on alternate days, starting from Raju?
Option 1: $15 \frac{9}{10}$ days
Option 2: $18 \frac{7}{10}$ days
Option 3: $21 \frac{7}{10}$ days
Option 4: $18 \frac{9}{10}$ days
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