# Learn Time And Work Concepts formula problems Time has always been an important tool for measuring the performance of a work. It is said that time is money. In business language, the expenditure on a certain project increases with the increase in time. So, doing a particular work in given interval of time increases the efficiency of work.We can say that time and work is closely related to each other.

## Understand the time and work concepts

When I was a student of class 6, I was given a small project of writing an article of 30 pages. The teacher ordered me to submit it after 3 days. Writing an article of 30 pages in 3 days is not an easy task for a student of class 6.I started working on it. There is a limit of doing work for every human being. I could write only 6 pages daily. So, according to me i would complete that project in 5 days. But, I had to complete that work in only 3 days. So, I decided to take help from Prince on this project. At last we both finished that project in 3 days. The teacher rewarded me a gift of Rs.500 for this work. I was happy but i wanted to share this money with Prince. Being a child i was confused about the part of Rs.500 which should be given to Prince. My father solved this problem. Can we now solve this problem with proper time and work concept. Its very basic problem to understand time and work concept.

I could complete the work in 5 days. So, My 1 day’s work=1/5 (By unitary method)
But we both completed in 3 days. So, Both one day’s work=1/3
Prince 1 days work=1/3 – 1/5 = 2/15
Prince alone could do it in 15/2=7.5 days.
Now, total prince work in 3 days = 3 * (2/15) = 6/15
And my total work in 3 days = 3 * (1/5) = 3/5
Their ratio of work = Prince:Mine = 2:3
Amount of money given to prince=(2/5) * 500=Rs 200.

### Alternate Method- time and work concepts

Since i could write 6 pages in 1 day.So,in 3 days i would write 18 pages.So,Prince has to write 12 pages to finish work.
Ratio of work=Prince:Mine = 12:18=2:3
Money to be given to prince=Rs 200.

IMPORTANT FORMULAE TO REMEMBER:-
• If a piece of work is done in N days.Total work done in 1 day = (1/N)
• If A does a work in X days and B in Y days.They both will finish in xy/(x+y) days.

Proof-A’s 1 day Work = 1/X and B’s 1 day work = 1/Y.

A+B 1 day work = (1/X + 1/Y)=(X + Y)/(XY)

Total number of days = Reciprocate above fraction = (XY)/(X+Y)
• In the case of Pipe and Cistern Same concept is used.
A Different Approach To Solve Time And Work Problems:-
Q.If A,B,C does a work in 5,10,15 days.Total time taken to do that work if they work together?
ANS-Take L.C.M of 5,10,15 = 15
Let there is 15 unit of work.
A does 3 unit in 1 day
B does 2 unit in 1 day
C does 1 unit in 1 day.

A+B+C 1 day work = 6 unit
So,total time taken in doing 15 unit = 15/6 =2.5 day

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