Formulas:
Work from Days:
If A does a work in "a" days, then in one day A does $\dfrac{1}{a}$ of
the work.
Calculate Percentage of Work:
Work to Percentage
=$\dfrac{1}{a}$*100
Percentage to work
=$\dfrac{1}{100}$*a
Formula:
Work done = Work Rate × Time
Ratio:
If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a work = 1 : 3.
Formula
If A can do a work in 10 days, in one day he can do 1/10th of the total work.
Simple! It can also be expressed in percentage
1/10*100 % or 10% of total work.
If A can do a work in 10 days, Then One day work of A = 1/10 of total work = 10% of total work.
Vice Versa, If A does 10% of work in day, he can complete the total work in 10 days.
Solved Examples - Easy
As No of men increase, time Reduces. Work rate is inversely
proportional to time.
No of Days 2 x .
No of Men 10 5 .
In inverse proportion, No of days X No of men is a constant. 2 * 10 = 5*x
So x = 4 days
Alternate method: Total work = 20 man days
If 5 men are working, it will take (20 man days/5 man) = 4 days
Work done - Formula
Solved Examples - Easy
A's one day work = 1/10
B's one day work = 3 times A's work rate = 3/10
Applying formula = 1/10*10 = 3/10 * x
x = 3.33 days
Total work is taken as 1 unit of work, when the work done is same for tow cases.
Working Together - Formula
If B does a work in b days, then in one day B does B= $\dfrac{1}{b}$ of the work.
Then, in one day, if A and B work together, then their combined work is $\dfrac{1}{a}$ + $\dfrac{1}{b}$ or $\dfrac{a+b}{ab}$
Solved Examples - 1
Here man's one day work and women's one day work is known.
One Man's one day work =1/(8*12) = 1/96
One Women's one day work = (1/20*10) =1/200
If they work together
Total work done done by 12 men and 15 women = 12*(1/96) + 15 * (1/200) = 0.2 of the work = 20%
So to complete 100% work = 100/20 = 5 days
Solved Examples - 2
Here man's one day work and women's one day work is known.
Let 1 mans 1 days work = x
1 womans 1 days work = y
Total work done by 4 men and 6 women in one day
= 4x + 6y = 1/8
Total work done by 3 men and 7 women in one day
= 3x + 7y = 1/10
x = 11/400 and y = 1/400 = 1 women's 1 day work
10 womens 1 days work = 10/400 = 1/40 of total work.
Hence 10 women will complete the work in 40 days.
Solved Examples - 3
Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 - 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18