(A + C)'s 1 day work = \(\cfrac { 1 }{ 6 } \) 
A's 1 day work = \(\cfrac { 1 }{ 12 } \) 
C's 1 day work = \(\cfrac { 1 }{ 6 } -\cfrac { 1 }{ 12 } =\cfrac { 2-1 }{ 12 } =\cfrac { 1 }{ 12 } \) 
(B + C)'s 1 day work = \(\cfrac { 1 }{ 3 } \) 
B's Iday work = \(\cfrac { 1 }{ 3 } -\cfrac { 1 }{ 12 } =\cfrac { 4-1 }{ 12 } =\cfrac { 3 }{ 12 } =\cfrac { 1 }{ 4 } \) 
B alone can complete the work in 4 hours.

Goods increase lorries also increase.
So, it is Direct variation.
The multiplying factor is \(\cfrac { 180 }{ 135 } \) 
Days decrease lorries increase
So it is indirect variation
The multiplying factor is \(\cfrac { 5 }{ 4 } \) 

4 more lorries are required to transport 180 tonnes of goods in 4 days. 

Number of Soaps increase, so the days also increase.
So it is direct variation
The multiplying factor is \(\cfrac { 14400 }{ 9600 } \) 
Time increase days decrease
So it is indirect variation
The multiplying factor is \(\cfrac { 15 }{ 18 } \) 

It will produce 14400 soaps in 7^1/2th days.

 Number of machines decrease so making cement bags also decrease.
So it is direct variation
The multiplying factor is \(\cfrac { 24 }{ 36 } \) 
Days increase so making cement bags also increase
So it is direct variation
The multiplying factor is \(\cfrac { 18 }{ 12 } \) 

7000 bags can be made in 18 days using 24 machines.

Days increase. So men will decrease
So, it is inverse proportion
The multiplying factor is \(\cfrac { 18 }{ 20 } \) 
Time increase, so men will decrease.
So, it is inverse proportion
The multiplying factor is \(\cfrac { 12 }{ 14 } \) 
 
162 men are required to finish the job 20 days working 14 hours a day.