Solution:

Let the amount of work done by a man in a day be ‘m’ and the amount of work done by a woman in a day be ‘w’.

Therefore, 4 men and 3 women will do 4m+3w amount of work in a day. If 4 men and 3 women complete the entire work in 6 days, they will complete (1/6)th of the work in a day.

Hence, 4m+3w=1/6 --------------- (1)    

and from statement (2), 5m+6w=1/4 ----------------- (2)

Solving eqn (1) and eqn (2), we get 3m=1/12 or m=1/36

. i.e. a man does (1/36)th of the work in a day. Hence he will take 36 days to do the work.

Substituting the value of m in eqn (1), we get 4×{1/36}+3w=1/6

⇒ 3w=1/6−1/9=3−{2/18}=118 or w=1/54

. i.e. a woman does (1/54)th of the work in a day. Hence she will take 54 days to do the entire work.

Solution:

Let 'f' m3/min be the filling capacity of the pump. 

Therefore, the emptying capacity of the pump will be =(f+10)m3/min.

The time taken to fill the tank will be=3600/f minutes

And the time taken to empty the tank will be 3600/f+10

.We know that it takes 12 more minutes to fill the tank than to empty it

i.e3600/f–3600/f+10=12

⇒ 3600f+36000−3600f=12(f2+10f)

⇒ 36000=12(f2+10f) ⇒ 3000=f2+10f 

⇒ f2+10f−3000=0.

Solving for positive value of 'f' we get, f=50.

Therefore, the emptying capacity of the pump =50+10= 60 m3/min

Solution:

Even before you start working on the problem, check out if you can eliminate some answer choices as impossible.

We know that if A and B alone work, they can complete the job in 6 days. Therefore, if all three of them A, B and C work together the number of days it will take to complete the job will surely be less than 6 days. Hence, we can eliminate answer choices (1) and (4) right away.

Let A be the number of days that A will take to complete the job alone, B days for B to complete the job alone and C days for C to complete the job alone.

A and B can do a job in 6 days. They complete (1/6)th of the job in a day. 

i.e.1/A+1/B=1/6 ------- -- (1)

Similarly, B and C will complete 1/10)th of the job in a day. 

i.e 1/B+1/C=1/10 ---------- (2)

And C and A will complete 

1/7.5

 or (2/15)th of the job in a day 

i.e 1/C+1/A=2/15 ------------ (3).Adding (1), (2) and (3) we get: 

1/A+1/B+1/B+1/C+1/C+1/A=1/6+110+2/15

 ⇒2/A+2/B+2/C={5+3+4}/30

⇒ 1/A+1/B+1/C=6/30=1/5

.i.e working together, A, B and C complete (1/5)th of the job in a day. 

Therefore, they will complete the job in 5 days.

Solution:

Now if we try to eliminate choices in this question, we know that A and B together take 6 days to complete the job. Therefore, A alone will take more than 6 days to complete the job. Therefore, we can eliminate answer choice (2).

In any question, as a rule spend about 5 seconds to see if the answer choices provide any clue to solve the question or help in eliminating one or more obviously absurd choices. This will help you (1) in reducing the time it will take to do the problem and (2) in increasing your probability of success should you choose to take a guess without actually solving the problem

Let A be the number of days that A will take to complete the job alone, B days for B to complete the job alone and C days for C to complete the job alone.

A and B can do a job in 6 days. They complete (1/6)th of the job in a day. 

i.e.1/A+1/B=1/6 ------- -- (1)

Similarly, B and C will complete (1/10)th of the job in a day. 

i.e 1/B+1/C=1/10 ---------- (2)

And C and A will complete 

1/7.5 or (2/15)th of the job in a day 

i.e 1/C+1/A=2/15 ------------ (3).

Subtracting eqn (2) from eqn (1) 

We get1/A−1/C=1/6−1/10=115  ----------- (4)

Adding eqn (4) and eqn (3) we get,1/A−1/C+1/A+1/C=2/A=1/15+2/15

=1/5

  ⇒ 1/A=1/10

 . i.e. A does 1/10

 of the job in a day and therefore, will take 10 days to complete the job working alone.

Solution:

Assume there are 360 units of work (LCM of 40,60 and 12). 

Hence, A,B and C can do 4,9 and 30 units per day or together 43 units every 3 days.

So In 24 days, 43×8=344 units of work is completed. In the next 2 days, 13 units are completed and on 27th day, C takes (1/10)th of a day to finish the rest.

So, A and B worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by C.

The wages shall also be distributed in the same ratio as:

Rs 36, Rs 81 and Rs 243