Question : A and B together can do a certain work in $x$ days. Working alone, A and B can do the same work in ($x$ + 8) and ($x$ + 18) days, respectively. A and B together will complete $\frac{5}{6}$th of the same work in:
Option 1: 12 days
Option 2: 8 days
Option 3: 10 days
Option 4: 9 days
Correct Answer: 10 days
Solution : According to the question, One day work of A = $\frac{1}{x + 8}$ work per day One day work of B = $\frac{1}{x + 18}$ work per day One day work of (A + B) = $\frac{1}{x}$ ⇒ $\frac{1}{x + 8 }$ + $\frac{1}{x + 18}$ = $\frac{1}{x}$ ⇒ $\frac{x + 18 + x + 8}{(x + 18)(x + 8)}$ = $\frac{1}{x}$ ⇒ $\frac{2x + 26}{(x + 18)(x + 8)}$ = $\frac{1}{x}$ ⇒ $2x^{2} + 26x = x^{2} + 26x + 144$ ⇒ $x^{2} − 144 = 0$ ⇒ $x = 12$ days $\therefore$ A and B together can finish $\frac{5}{6}$th of the work in $12 × \frac{5}{6}$ = 10 Hence, the correct answer is 10 days.
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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:
Option 1: 9 days
Option 2: 12 days
Option 4: 8 days
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:
Option 1: 6 days
Option 3: 5 days
Option 4: 4 days
Question : A can do $\frac{2}{5}$ of a work in 12 days while B can do $66 \frac{2}{3}\%$ of the same work in 16 days. They work together for 10 days. B alone will complete the remaining work in:
Option 2: 4 days
Option 3: 8 days
Question : A alone can complete a work in 18 days and B alone in 15 days. B alone worked at it for 10 days and then left the work. In how many more days, will A alone complete the remaining work?
Option 1: $5$ days
Option 2: $5\frac{1}{2}$ days
Option 3: $6$ days
Option 4: $8$ days
Question : A can-do $\frac{1}{5}$ of a piece of work in 20 days, B can do 30% of the same work in 36 days, and C can do 80% of the same work in 160 days. B and C together started and worked for x days. After x days B left the work, and A joined C and both completed the remaining work in (x - 41) days. If the ratio between the work done by (B + C) together to the work done by (A + C) together is 19: 6, then what fraction of the same work can be completed by C alone in 2x days?
Option 1: $\frac{57}{100}$
Option 2: $\frac{13}{25}$
Option 3: $\frac{19}{25}$
Option 4: $\frac{6}{25}$
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