Efficiency of Raj = ¹⁰⁰/₂₀ = 5%

Work completed by Raj = 25%

Rest work = 75%

Efficiency of Abhijit = ⁷⁵/₁₀ = 7.5%

Combined efficiency = 5 + 7.5 = 12.5%

They will complete the whole work by working together in,

= ¹⁰⁰/_12.5 = 8 days.

Pipe A can fill the empty tank in = 0.9 hours

So work rate of the Pipe A = ¹⁰⁰/_0.9 % per hour.

Pipe B can empty the tank in = 0.7 hours

Negative Work rate of B = ¹⁰⁰/_0.7 % per hour. (B is removing water, so, taken as negative work.)

Tank fill per hour = ¹⁰⁰/_0.7 - ¹⁰⁰/_0.9 = 31.75% per hour.

Time Taken to empty the tank = ¹⁰⁰/_31.75 = 3.14 hours.

So, Capacity of the tank = 3.14 * 180 = 567 liters.

\begin{align} & {\text{Whole}}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{in}} \cr & = \left( {20 \times \frac{5}{4}} \right) = 25\, {\text{days}} \cr & {\text{Now}}, \, \left( {1 - \frac{4}{5}} \right)\, \, i.e., \cr & \frac{1}{5}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{and}}\, {\text{B}}\, {\text{in}}\, {\text{3}}\, {\text{days}} \cr & {\text{Whole}}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{done}}\, {\text{by}}\, {\text{A}}\, {\text{and}}\, {\text{B}}\, {\text{in}} \cr & = \left( {3 \times 5} \right) = 15\, {\text{days}} \cr & {\text{A's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{25}}, \cr & \left( {{\text{A + B}}} \right)\, {\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{15}} \cr & \therefore {\text{B's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{15}} - \frac{1}{{25}}} \right) = \frac{4}{{150}} = \frac{2}{{75}} \cr & {\text{So, }}\, {\text{B}}\, \, {\text{alone}}\, {\text{would}}\, {\text{do}}\, {\text{the}}\, {\text{work}}\, {\text{in}} \cr & \frac{{75}}{2} = 37\frac{1}{2}\, {\text{days}} \cr\end{align}

\begin{align} & {\text{One}}\, {\text{day's}}\, {\text{work}}\, {\text{of}} \cr & \left( {A + B} \right) = \frac{1}{{18}}\, .....(1) \cr & {\text{One}}\, {\text{day's}}\, {\text{work}}\, {\text{of}} \cr & \left( {A + C} \right) = \frac{1}{{12}}\, .....\left( 2 \right) \cr & {\text{One}}\, {\text{day's}}\, {\text{work}}\, {\text{of}} \cr & \left( {B + C} \right) = \frac{1}{9}\, .....\left( 3 \right) \cr & {\text{Adding}}\, \left( {\text{1}} \right){\text{, }}\, \left( {\text{2}} \right)\, {\text{and}}\, \left( {\text{3}} \right) \cr & 2 \times \left( {A + B + C} \right) \cr & = \left\{ {\left( {\frac{1}{{18}}} \right) + \left( {\frac{1}{{12}}} \right) + \left( {\frac{1}{9}} \right)} \right\} \cr & = \frac{1}{4} \cr & {\text{One day's work of}} \cr & \left( {A + B + C} \right) = \frac{1}{8} \cr & B = \left( {\frac{1}{8}} \right) - \left( {A + C} \right) \cr & B = \left( {\frac{1}{8}} \right) - \left( {\frac{1}{{12}}} \right) \cr & {\text{One day's work of}} \cr & B = \frac{{\left( {3 - 2} \right)}}{{24}} = \frac{1}{{24}} \cr & B\, {\text{need}}\, 24\, {\text{days}} \cr\end{align}

Given,

A is 60% more efficient of B. Means,

A = B + 60% of B.

A = (⁸/₅)B.

A can complete whole work in 15 days, So,

One day work of A = ¹/₁₅.

One day work of ^8B/₅ = ¹/₁₅

One day work of B = ⁵/₁₂₀ = ¹/₂₄.

One day work, (A + B),

= (¹/₁₅) + (¹/₂₄)

One day work, (A + B) = ^(24+15)/₃₆₀ = ³⁹/₃₆₀. So, Time taken to finish the work by A and B together = ³⁶⁰/₃₉ = ¹²⁰/₁₃.

Alternatively

> We can solve it through percentage method.

Given,

A = ^8B/₅

A can complete whole work in 15 days.

Work rate of A = ¹⁰⁰/₁₅ = 6.66% per day.

Work rate of ^8B/₅ = 6.66%

Work rate of B = 4.16% per day.

Work rate of (A + B) = 6.66 + 4.16 = 10.82% per day.

So, A and B can complete 100% work