\begin{align} & \left( {{\text{B + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{9} + \frac{1}{{12}}} \right) = \frac{7}{{36}} \cr & {\text{Work}}\, {\text{done}}\, {\text{by}}\, {\text{B}}\, {\text{and}}\, {\text{C}}\, {\text{in}}\, {\text{3}}\, {\text{days}} \cr & = \left( {\frac{7}{{36}} \times 3} \right) = \frac{7}{{12}} \cr & {\text{Remaining}}\, {\text{work}} \cr & = \left( {1 - \frac{7}{{12}}} \right) = \frac{5}{{12}} \cr & {\text{Now}}, \, \frac{1}{{24}}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{in}}\, {\text{1}}\, {\text{day}} \cr & {\text{So}}, \, \frac{5}{{12}}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{in}} \cr & \left( {24 \times \frac{5}{{12}}} \right) = 10\, {\text{days}} \cr\end{align}

\begin{align} & {\text{Ration}}\, {\text{of}}\, {\text{rates}}\, {\text{of}}\, {\text{working}}\, {\text{of}}\, {\text{A}}\, {\text{and}}\, {\text{B}} \cr & = 2:1 \cr & {\text{So, }}\, {\text{ratio}}\, {\text{of}}\, {\text{times}}\, {\text{taken}} = 1:2 \cr & {\text{B's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{12}} \cr & \therefore {\text{A's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \frac{1}{3};\, ({\text{2times}}\, {\text{of}}\, {\text{B's}}\, {\text{work}}) \cr & \left( {{\text{A + B}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{6} + \frac{1}{{12}}} \right) = \frac{3}{{12}} = \frac{1}{4} \cr & {\text{So, }}\, {\text{A}}\, {\text{and}}\, {\text{B}}\, {\text{together}}\, {\text{can}}\, {\text{finish}}\, {\text{the}} \cr & {\text{work}}\, {\text{in}}\, {\text{4}}\, {\text{days}}{\text{.}}\, \cr\end{align}

⁷/₁₀ part of work has been completed by A in 15 days. Then,

Rest work = 1 - (⁷/₁₀) = ³/₁₀ part.

Given, That ³/₁₀ part of the work is completed by A and B together in 4 days. Means,

(A+B) completed the ³/₁₀ of work in 4 days.

So, (A+B)'s 1 day's work = ³/_(10*4) = ³/₄₀;

Hence,

(A+B) can complete the work in ⁴⁰/₃ = 13(¹/₃) days.

X completes ¹/₃^rd in 4 days = 33.33 % job in 4 days.

X One day work = 8.33%

Y one day work = 5.55% [As he complete ¹/₆ job = 16.66 % job in 3 days]

Z one day work = 10%

Work done in 3 days by X, Y and Z

= 25 + 16.66 + 30 = 71.66 %

Remaining work will be done by Y in,

^28.33/_5.55 = 5.1 days.

Assume work to be done 100%.

First case,

A + B = ¹⁰⁰/₅ =20% work done per day -------- (1)

Second case,

2A + ^B/₂ = ¹⁰⁰/₄ = 25% work done per day ------ (2)

On solving equation (1) and (2), we get

A = 10 days.