\begin{align} & {\text{work}}\, {\text{done}}\, {\text{by}}\, {\text{X}}\, {\text{in}}\, {\text{4}}\, {\text{days}} \cr & = \left( {\frac{1}{{20}} \times 4} \right) = \frac{1}{5} \cr & {\text{Remaining}}\, {\text{work}} \cr & = \left( {1 - \frac{1}{5}} \right) = \frac{4}{5} \cr & \left( {{\text{X + Y}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{20}} + \frac{1}{{12}}} \right) = \frac{8}{{60}} = \frac{2}{{15}} \cr & {\text{Now}}, \frac{2}{{15}}{\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{X}}\, {\text{and}}\, {\text{Y}}\, {\text{in}}\, {\text{1}}\, {\text{day}}. \cr & {\text{So}}, \, \frac{4}{5}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{done}}\, {\text{by}}\, {\text{X}}\, {\text{and}}\, {\text{Y}}\, {\text{in}} \cr & \left( {\frac{{15}}{2} \times \frac{4}{5}} \right) = 6\, {\text{days}} \cr & {\text{Hence, }}\, {\text{total}}\, {\text{time}}\, {\text{taken}} \cr & = \left( {6 + 4} \right)\, {\text{days}} \cr & = 10\, {\text{days}} \cr\end{align}

\begin{align} & {\text{Let}}\, {\text{1}}\, {\text{man's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = x\, {\text{and}} \cr & 1\, {\text{boy's}}\, {\text{1day's}}\, {\text{work}} = y \cr & {\text{Then, }}\, 6x + 8y = \frac{1}{{10}}\, {\text{and}}\, \cr & 26x + 48y = \frac{1}{2} \cr & {\text{Solving}}\, {\text{these}}\, {\text{two}}\, {\text{equations, }}\, {\text{we}}\, {\text{get}} \cr & x = \frac{1}{{100}}\, and\, y = \frac{1}{{200}} \cr & {\text{(15}}\, {\text{men}}\, {\text{ + 20}}\, {\text{boy)'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{{15}}{{100}} + \frac{{20}}{{200}}} \right) = \frac{1}{4} \cr & \therefore {\text{15}}\, {\text{men}}\, {\text{and}}\, {\text{20}}\, {\text{boys}}\, {\text{can}}\, {\text{do}}\, {\text{the}}\, {\text{work}}\, {\text{in}}\, {\text{4}}\, {\text{days}} \cr\end{align}

Efficiency of pipe A,

¹⁰⁰/₂₀ = 5%

20% of efficiency of A = 1%

Then, efficiency of 5 such pipes = 5%.

Then,

Time taken to fill the tank = ¹⁰⁰/₅ = 20 min.

Water filled by (boy + girl) in one minute,

⁴/₃ + ³/₄ = ⁽¹⁶⁺⁹⁾/₁₂ = ²⁵/₁₂ liter;

Hence, time taken to fill 100 liter,

= 100 * ¹²/₂₅ = 48 minutes.

Formula: If A can do a piece of work in n days, then A's 1 day's work = ¹/_n. \begin{align} & (A + B + C)'s\, 1\, {\text{day's work}} \cr & = \left( {\frac{1}{{24}} + \frac{1}{6} + \frac{1}{{12}}} \right) = \frac{7}{{24}} \cr\end{align} Formula: If A's 1 day's work = ¹/_n, then A can finish the work in n days.

So, all the three together will complete the job in $\left( {\frac{{24}}{7}} \right){\text{days}} = 3\frac{3}{7}{\text{days}}$