# Work Problem Basics

Work problem is another common topic tested during GMAT . About 2-4 questions are asked from this topic. Work is a specific task assigned to one or more persons that are required to be completed in 'n' amount of time.

Here n is represented as days.

Suppose Jim works for N days then he can do 1/N of the work in 1 day
Suppose Tim work for M days then he can do 1/M of the work in 1 day

Now if Jim and Tim works together for 1 day then they can do ( 1/N + 1/M ) work in 1 day

So in 1 day then can do (M+N)/M*N

Now lets plug in some real numbers

N=10

M=20

In 1 day Jim and Tim can do 30/200 of the total work, represented as (30/200 )* W
where 'W' is the total work.

(30/200) x w = 1 day

So W will be completed in (1 * 200)/30  days

Note :This is the reciprocal of the fraction of work that is completed in 1 day

The work problems involves multiple workers working for many days. In these scenarios remember the formula

Work Done = W/(M*D*H)

Where W is the total work done , M is the number of men involved in the work , D is the number of days to complete the work and H the number of hours put in by the workers.

Q: 15 men working 4 hours a day can completely build a swimming pool with length 100 meters, breadth 50 meters and height 10 meters in 10 days. How many days will 25 men working 10 hours a day required to build a swimming pool with length 50 meters ,breadth 25 meters and height 5 meters.

Solution :This problem can be directly solved using the formula mentioned above.

Only thing to note here is that W = Volume of the swimming pool that is being created

15 men 4 hours/day 10 days        -------> W = 100*50*10
25 men 10 hours/day n days        -------> W = 50*25*5

Now equating using the formula W/(M*D*H) we can write

(100*50*10)/(15*10*4) = (50*25*5)/(25*10*n)

n = 3/10 days

Therefore the total number of days to complete a swimming pool with length 50 meters ,breadth 25 meters and height 5 meters is 0.3 days(3/10)

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