Question : A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying; how many days must A work alone to complete the remaining work?
Option 1: $7\ \text{days}$
Option 2: $7\frac{1}{3}\ \text{days}$
Option 3: $7\frac{2}{3}\ \text{days}$
Option 4: $8\ \text{days}$
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Correct Answer: $7\frac{1}{3}\ \text{days}$
Solution : Time taken by A alone to do the work = 8 days Part of work done by A alone in a day = $\frac{1}{8}$ Time taken by B alone to destroy the work = 3 days Part of work destroyed by B alone in a day = $\frac{1}{3}$ Part of work done by A in 6 days = $\frac{6}{8}$ Part of work destroyed by B in last 2 days = $\frac{2}{3}$ Part of work completed after 6 days = $\frac{6}{8}-\frac{2}{3}$ = $\frac{18-16}{24}$ = $\frac{2}{24}$ Remaining part of work to be completed by A alone = $1-\frac{2}{24}$ = $\frac{22}{24}$ So, the number of days needed to complete the remaining work by A alone = $\frac{\frac{22}{24}}{\frac{1}{8}}$ = $\frac{22}{3}$ = $7\frac{1}{3}\ \text{days}$ Hence, the correct answer is $7\frac{1}{3}\ \text{days}$.
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Question : A piece of work can be completed by P and Q together in 24 days, and the same piece of work can be completed by R alone in 60 days. If P and R together can do the same work in 36 days, then find the time taken by Q to complete this piece of work alone.
Option 1: $8\frac{4}{5}$days
Option 2: $29\frac{9}{13}$days
Option 3: $3\frac{6}{7}$days
Option 4: $32\frac{8}{11}$days
Question : A can do a piece of work alone in 15 days, while B complete the same piece of work alone in 12 days. If they work on it together for 5 days, then the fraction of the work that will be left is:
Option 1: $\frac{3}{4}$
Option 2: $\frac{5}{8}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{5}{7}$
Question : A alone can do a piece of work in 10 days. B alone can do the same work in 12 days. They work on alternate days starting with A. In how many days will they complete $\frac{3}{4}$th of the total work?
Option 1: $\frac{47}{3}$ days
Option 2: $\frac{50}{3}$ days
Option 3: $\frac{53}{6}$ days
Option 4: $\frac{49}{6}$ days
Question : Seema alone can do a piece of work in 8 days and her sister Reema alone can do the same work in 24 days. If they worked together, then in how many days they will complete the work?
Option 1: 8 days
Option 2: 6 days
Option 3: 10 days
Option 4: 4 days
Question : Aadish can complete a work in 14 days. If he worked for 8 days, then what fraction of the work would be left?
Option 1: $\frac{2}{7}$
Option 2: $\frac{3}{7}$
Option 3: $\frac{4}{7}$
Option 4: $\frac{1}{7}$
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