Question : Ramesh does half as much work as Parul in $\frac{4}{5}$ of the time. If together Ramesh and Parul take 24 days to complete the work, then how much time will Parul take to do it?
Option 1: 38 days
Option 2: 41 days
Option 3: 37 days
Option 4: 39 days
Correct Answer: 39 days
Solution : Let the time taken by Parul to complete the work be $x$. Part of work done by Parul in a day = $\frac{1}{x}$ Time taken by Ramesh $=2×\frac{4x}{5} = \frac{8x}{5}$ Part of work done by Ramesh in a day = $\frac{5}{8x}$ Time taken by Ramesh and Parul together to complete the work = 24 days Part of the work done by Ramesh and Parul together in a day = $\frac{1}{24}$ $\frac{1}{x}+\frac{5}{8x}=\frac{1}{24}$ ⇒ $\frac{8+5}{8x}=\frac{1}{24}$ ⇒ $x = 3 × 13 = 39$ days Hence, the correct answer is 39 days.
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Question : To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is:
Option 1: 22 days
Option 2: 24 days
Option 3: 30 days
Option 4: 20 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 2: 8 days
Option 3: 5 days
Option 4: 4 days
Question : A can complete a work in 8 days and B can complete the same work in 11 days. How many days will they take, if both work together?
Option 1: $4 \frac{12}{17}$
Option 2: $5 \frac{12}{19}$
Option 3: $4 \frac{11}{19}$
Option 4: $4 \frac{12}{19}$
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
Question : To do a certain task X would take 3 times as long as Y and Z together, and Z would take 4 times as long as Y and X together. Three of them together can complete the task in 10 days. How much time is taken by X and Z to complete the task?
Option 1: $18 \frac{2}{9}$ days
Option 2: $20 \frac{1}{9}$ days
Option 3: $21 \frac{1}{9}$ days
Option 4: $22 \frac{2}{9}$ days
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