A    :    B    :    C   

Ratio of efficiency               3     :    1    :    2   

Ratio of No.of days            1/3  :   1/1  :   1/2    

     or                                       2    :    6    :    3   

Hence A is correct.  

Sol : In this kind of questions we find the work force required to complete the work in 1 day (or given unit of time) then we equate the work force to find the relationship between the efficiencies (or work rate) between the different workers.

Therefore, 6B+8G = 6 days

 => 6(6B+8G)= 1 day  (inversely proportional)

 => 36B+48G =1         ( by unitary method)

Again  14B+10G = 4days

 => 56B+40G =1

so, here it is clear that either we employ 36B and 48G to finish the work in 1 day or 56B and 40G to finish the same job in 1 day. thus , we can say

 => 36B+48G = 56B+40G

 => G= 2.5B

Thus a Girl is 2.5 times as efficient as a boy.

Now, since  36B+48G = 1

 => 36B+48(2.5 B)=1

 =>156B=1

i.e., to finish the job in 1 day 156 boys are required or the amount of work is 156 boys-days

Again    1G+1B=2.5B+1B=3.5B

Now, since 156 boys can finish the job in 1 day

so 1 boy can finish the job in 156 days

Therefore, 3.5 boys can finish the job in 1×1563.5= 47 days.

Number of persons * days = work  

20 * 7 = 140 man- days 

Now,  x * 28  = 140 men- days

=> x =5         

Therefore in second case the required number of person is 5.

Second method:

Since work is constant, therefore  M1 x D1= M2 x D2

20 x 7 = M2 x 28

=> M2 = 5 

Filling efficiency = 5%        

Emptying efficiency = 1.66%  

Net efficiency = 5-1.66 = 3.33%

Therefore, Required time to fil the tub =100/3.33= 30 minutes

Ratio of times taken by A and B = 1 : 2.

The time difference is (2 - 1) 1 day while B take 2 days and A takes 1 day.

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/60

(A + B)'s 1 day's work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

A's 1 days work = 1/12 

B's 1 days work =1/6

Therefore, (A+B)'s 1 day's work= 1/12 + 1/6 = 1/4       

Therefore, Time taken by both to finish the whole work = 114 = 4 days

Alternatively :

Efficiency of A =100/12 =8.33%

Efficiency of B =100/6=16.66%

Combined efficiency of A and B both = 8.33+16.66=25%

Therefore, Time taken by both to finish the work (working together) =100/25= 4days

Let quantity of mixture be x liters.

Suppose a container contains x units of liquid from which y units are taken out and replaced by Water. After operations , the quantity of pure liquid = x1-yxn units, Where n = no of operations . 

So, Quantity of Milk = x1-6x2  

Given that, Milk : Water = 9 : 16 

=> Milk : (Milk + Water) = 9 : (9+16)

=> Milk : Mixture = 9 : 25 

 Therefore, x1-6x2x=925

=> x = 15 liters

pool : kerosene 

   3  :  2(initially) 

   2  :  3(after replacement)

 Remaining QuantityInitial Quantity=1-Replaced QuantityTotal Quantity

(for petrol)   23=1-10k

 => K = 30

 Therefore the total quantity of the mixture in the container is 30 liters.