Question : A can do $\frac{7}{8}$ of work in 28 days, and B can do $\frac{5}{6}$ of the same work in 20 days. The number of days they will take to complete if they do it together is:
Option 1: $15\frac{3}{7}$ days
Option 2: $17\frac{3}{5}$ days
Option 3: $14\frac{5}{7}$ days
Option 4: $13\frac{5}{7}$ days
Correct Answer: $13\frac{5}{7}$ days
Solution : Time taken by A alone to complete $\frac{7}{8}$ of a work = 28 days Time taken by A alone to complete the work = $28 × \frac{8}{7}$ days = 32 days ⇒ Part of work done by A alone in a day = $\frac{1}{32}$ Time taken by B alone to complete $\frac{5}{6}$ of the work = 20 days Time taken by B alone to complete the work = $20 ×\frac{6}{5}$ = 24 days ⇒ Part of work done by B alone in a day = $\frac{1}{24}$ Let the time taken by A and B together to complete the work = $x$ ⇒ Part of work done by A and B in a day = $\frac{1}{x}$ ⇒ $\frac{1}{32}$ + $\frac{1}{24}$ = $\frac{1}{x}$ ⇒ $\frac{3+4}{96}$ = $\frac{1}{x}$ ⇒ $x$ = $\frac{96}{7}$ = $13 \frac{5}{7}$ days Hence, the correct answer is $13\frac{5}{7}$ days.
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Question : A can do $\frac{4}{5}$th of a work in 20 days and B can do $\frac{3}{4}$th of the same work in 15 days. They work together for 10 days. C alone completes the remaining work in 1 day. B and C together can complete $\frac{3}{4}$th of the same work in:
Question : A can do $\frac{2}{5}$ of a work in 6 days and B can do $\frac{2}{3}$ of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:
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Question : A can complete $\frac{2}{3}$ of a work in 4 days and B can complete $\frac{3}{5}$ of the work in 6 days. In how many days can both A and B together complete the work?
Question : Tom can do a piece of work in 7 days, whereas Jay can do the same work in 14 days. How long will it take to finish the work if both work together?
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