Question : If $x$ men can do a piece of work in $x$ days, then the number of days in which $y$ men can do the same work is:

Option 1: $xy$ days

Option 2: $\frac{y^{2}}{x}$ days

Option 3: $\frac{x^{2}}{y}$ days

Option 4: $x^{2}y$ days

Question : A can do $\frac{1}{3}$rd of a piece of work in 32 days, B can do $37 \frac{1}{2}$% of the same work in 24 days, while C can do 60% of the same work in 48 days. B and C together started and worked for x days. After x days, B left and A joined C and together, completed the remaining work in (x + 8) days. If the ratio of the work done by (B + C) together to the work done by (A + C) together is 9 : 11, then what fraction of the same work can be completed by C alone in 3.5x days?

Option 1: $\frac{18}{25}$

Option 2: $\frac{4}{5}$

Option 3: $\frac{7}{10}$

Option 4: $\frac{3}{4}$

Question : Simplify $\frac{1}{2 + 2 p} + \frac{1}{2 + 2 q} + \frac{1}{2 + 2 r}$, where $p = \frac{x}{y + z}$, if $q = \frac{y}{z + x}$ and $r = \frac{z}{x + y}$.

Option 1: $1$

Option 2: $x+y+z$

Option 3: $2$

Option 4: $\frac{1}{2}$

Question : A alone can do a work in 14 days. B alone can do the same work in 28 days. C alone can do the same work in 56 days. They started the work together and completed the work such that B was not working in the last 2 days and A did not work in the last 3 days. In how many days (total) was the work completed?

Option 1: $\frac{82}{7}$ days

Option 2: $\frac{79}{7}$ days

Option 3: $\frac{65}{7}$ days

Option 4: $\frac{72}{7}$ days

Question : A can do a piece of work in 9 days, while B can do it in 12 days. A and B together can do the work in:

Option 1: $5\frac{1}{7}$ days

Option 2: $5\frac{2}{7}$ days

Option 3: $6\frac{1}{7}$ days

Option 4: $6\frac{2}{7}$ days