Shortcut 68:
Three men working together
$\frac{ABC}{AB+BC+AC}$
Question:
A can do a work in 40 days, B in 50 days and C in 60 days. If they work together, how long will they take to complete the work?
A = 40
B = 50
C = 60
Substitute the values in the above formula, we get
Time taken together = (40 x 50 x 60)/(40 + 50 + 60)
= 16.21 days

Shortcut 69:
Work done
Work Done=per day work*number of days
Question:
A can do a piece of work in 40 days. What is the fraction of work done by him in 25 days?
Per day work of A = 1/40
Number of days for which A worked = 25
Work done = (1/40) x 25
= 5/8

Shortcut 70:
Remaining work
$Remaining work=1-work done$
Question:
A can do a work in 30 days, B in 40 days. A works for 9 days and the remaining work is done by B. What is the total number of days to complete the work?
Time taken to complete the work
= Remaining work x time to finish full work
Remaining work for B = 1 – Work done by A
Work done by A = (1/30) x 9 = 3/10
Remaining work for B = 1 – 3/10 = 7/10
Time taken by B to complete the remaining work
= 7/10 x 40
= 28 days
Total time taken = 28 + 9 = 37 days

Shortcut 71:
Salary ratio of two men working together
$S_A:S_B=B:A$
Question:
A can do a work in 20 days and B can do the same work in 40 days. They both work together and get a combined salary of Rs. 3000. What is the salary of A?
SA = Salary of A
SB = Salary of B
A = 20; B = 40
SA : SB = 40 : 20 = 2 : 1
SA = [2/(2+1)] x 3000
= 2000
Salary of A = Rs. 2000

Shortcut 72:
Salary ratio of three men working together
$S_A:S_B:S_c=\frac1A:\frac1B:\frac1C$
Question:
A can do a work in 30 days B in 40 days and C in 50 days. If they all work together, what will the ratio between their salaries?