1. If A can do a piece of work in n days, then A's 1 day's work = 1/n
2. If A's 1 day's work = 1/n, then A can finish the work in n days
3. If A is thrice as good as in work B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of time taken by A and B to finish a work = 1 : 3.
4. Short Tricks
If M1 can do a W1 work in D1 days working H1 hour per day
and M2 can do a W2 work in D2 days working H2 hour per day, Then
M1D1W2 = M2D2W1
M1D1T1W2 = M2D2T2W1 (When time is given)
M1D1T1E1W2 = M2D2T2E2W1 (When efficiency is added)
M = Person
D = Days
W = Work
T = Time
E = Efficiency
1. 

A and B can do (1/20)th and (1/30)th part of total work in a day respectively.
in 8 days they can do 8(1/20 + 1/30) = 8/12 = (2/3)rd of the total work.
So, C has to do (1/3)rd of total work.
his share is (1/3)rd of total money. i.e. (1/3) X 1170 = 390
2. 

Ajay can do the work in 16 days.
so , ajay's one day's work = (1/16)th of the work.
in 4 days he can do (4 X 1)/16 = (1/4)th of the work.
Bharat has to do 1  (1/4) = 3/4 of the work.
so, To do 3/4th of the work he takes (3/4) X 24 = 18 days.
Total days = 4 +18 = 22 days
3. 

P can do (1/28)th of the work in a day i.e. in 7 days he completes (1/28) X 7 = (1/4)th of the work.
the remaining part of work (i.e. 3/4 of the work) is completed by P and Q working together at rate of (1/28 + 1/56) = 3/56 of the par day.
so , they take (3/4) X (56/3) = 14 days more to complete remaining work together.
4. 

P can do (1/4)th the work in 1 day and Q can do (1/12)th of the work in 1 day.
if they work for x days together,they complete x{1/4 + 1/12}th of work i.e. (x/3)rd of work.
So, {1  x/3} work is done by Q alone.
He completes this work in {(3  x)/3 X 12} = (12  4x) days.
Total no. of days taken x + (12  4x) = 6 days.
So, x = 2 days, P quits after 2 days.
5. 

Initially let the amount of work be x units which A, B, C do in 6, 9,12 days respectively.
A does x/6 units of work in a day.
B does x/9 units of work in a day.
C does x/12 units of work in a day.
So, they can do {x/6 + x/9 + x/12} units of work by working together in 1 day.
In 24 days the amount of work done = 24 X (13x/36) = 26x/3 units.
B can do 26x/3 units of work done by in 26x X 9/3x = 78 days.
B can complete in 78 days.
6. 

Let 5 people do the work in x days. Then 9 people will do the work in (x  12) days.
But, work done by both sets of people is the same
So, 5 X x = 9(x  12)
5x = 9x  108
x = 27 days
If 3 people take y days, then 5 X 27 = 3 X y
y = 45 days.
7. 

Let, A takes x days for complete work then B takes (x + 18) days for complete work.
A is thrice more efficient than B.
So, M1D1 = M2D2
3 X x = 1 X (x + 18)
2x = 18
x = 9
A takes 9 days and B takes (9 + 18) days.
They work together = 1/9 + 1/18 = 4/27
They finish work 27/4 days.
8. 

P and Q can do (1/10)th and (1/15)th of the total work in la day respectively.
In 6 days, they do (3/10 + 3/15)th of the total work i.e. (1/2) of the total work.
So, they complete the work in 12 days
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