Question : X can do a piece of work in $p$ days and Y can do the same work in $q$ days. Then the number of days in which X and Y can together do that work is:
Option 1: $\frac{p+q}{2}$
Option 2: $\frac{1}{p}$ + $\frac{1}{q}$
Option 3: $\frac{pq}{p+q}$
Option 4: $pq$
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Correct Answer: $\frac{pq}{p+q}$
Solution : Given: X can do a piece of work in $p$ days and Y can do the same work in $q$ days. X can do a piece of work in $p$ days ⇒ X in 1 day can do $\frac{1}{p}$ part of the work and Y can do a piece of work in $q$ days ⇒ Y in 1 day can do $\frac{1}{q}$ part of the work So, X and Y together in 1 day can do ($\frac{1}{p}$ + $\frac{1}{q}$) = $\frac{q + p}{pq}$ part of the work Therefore, X and Y can together do that work in (1 ÷ $\frac{q+p}{pq}$) = $\frac{pq}{p+q}$ days. Hence, the correct answer is $\frac{pq}{p+q}$ days.
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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
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