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Let us try to understand the basic concept of work and time with the example of construction of a building. To complete the construction in stipulated time few points are to be noted,
In the exam, we need to calculate the following in work and time questions
One of the methods is to use the days as denominator while solving the questions. But, the best trick is to find the efficiency of the workers in percentage. When we say X can complete a given work in 2 days, it means that C complete 50% of the work in one day. The following table can be used to calculate the efficiency in percentage.
Days to complete work | Work completed in one day | Efficiency in percentage |
---|---|---|
x | % | |
1 | 100% | |
2 | 50% | |
3 | 33.33% | |
4 | 25% | |
5 | 20% | |
6 | 16.6% | |
7 | 14.2% | |
8 | 12.5% | |
9 | 11.1% | |
10 | 10% | |
11 | 9.09% |
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The following are few formulae and short tricks for solving questions relating to work and time:
Formula 1:
If M1 persons can do W1 work in D1 days working T1 hours a day and M2 persons can do W2 work in D2 days working T2 hours a day then M1W2D1T1= M2W1D2T2.
For more clarity on this formula click here... Proportionality concept
Example: 5 people can finish 10 projects in 6 days working 6 hours a day. In how many days can 12 men complete 16 projects working 8 hours a day?
Solution: According to the above given formula, If M1 persons can do W1 work in D1 days working T1 hours a day and M2 persons can do W2 work in D2 days working T2 hours a day then,
M1W2D1T1 = M2W1D2T2
Hence, 16 projects can be completed in 3 days by 12 men working 8 hours a day
Formula 2:
If person P can do a work in x days and person Q can do the same work in y days then, one day work of P and Q together is
Example: If P can do a work in 5 days and Q can do a work in 7 days, then in how many days will P and Q working together will do the same work?
Solution: According to the above given formula, If person P can do a work in x days and person Q can do the same work in y days then, one day work of P and Q together is
so,
Hence, is both of them work together, work will be completed in 0.4 days
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Formula 3:
P and Q can do a work in x days, Q and R can do the same work in y days, P and R can do it in z days. If they all work together P, Q, R can do that work in
Example: If P, Q, R can do a piece of work in 6 days, 12 days and 5 days respectively. If all of them work together, how long will they take to complete the work?
Solution: According to the above given formula, P and Q can do a work in x days, Q and R can do the same work in y days, P and R can do it in z days. If they all work together P, Q, R can do that work in days.
So,
Hence, if all of them work together, the work will be completed in 2.22 days
Formula 4:
Consider P and Q two persons doing a work. If P takes x days more to complete a work than the time taken by (P+Q) to do the same work and Q takes y days more than the time taken by (P+Q) to do the same work, then (P+Q) together complete the same work in √xy days.
Example: Diya and Piya a completing some work. If Diya takes 9 days more to complete a work than the time taken by Piya and DIya together; Piya takes 4 days more than the time taken by DIya and Piya together, Then the time taken by both to finish the work is?
Solution: According to the above given formula, If P takes x days more to complete a work than the time taken by (P+Q) to do the same work and Q takes y days more than the time taken by (P+Q) to do the same work, then (P+Q) together complete the same work in √xy days..
so the time taken by both Diya and Piya to complete the work is
Formula 5:
Consider P and Q are two persons doing a work in a and b days respectively. Both begin together but if,
Example: Rani and Neetu are doing some work. Rani can complete a piece of work in 10 days while Neetu can complete the same work in 15 days. Initially they begin together but 5 days before the completion of the work Rani has to leave. Find the total number of days for the completion of the work.
Solution: According to the above given formula, when two perons begin together but on person has to leave , then the total time for completion of the work can be calculated by days
Here a= 10 days; b=15 days; x=5; T=?
Hence, total number of days to complete the work is 9 days.
Formula 6:
P and Q do a work in a and b days respectively. Both begin together, but after some days P leaves and the remaining work is completed by Q alone in x days. The time after which P left is, days.
Example: A and B do a piece of work in 40 days and 60 days respectively. Both begin together but after few days A has to leave. The remaining work is ompleted by B alone in 25 days. After how many days did A leave?
Solution: Given a=40 days, b=60 days, x=25 days. t=?
According to the formula, days.
Hence, A left after 14 days
Formula 7:
If A and B can complete the work in x days and A alone can do the same work in y days, the the time taken by B to complete the same work will be given by days.
Example: A can complete a piece of work in 12 days. A and B together can complete the same work in 8 days. In how many days, can B alone complete the same peice of work?
Solution: Given x=8 days, y=12 days
According to the formula, days
Hence, B alone can complete the work in 24 days.
Formula 8:
If A and B working together, can finish a piece of work in x days, B and C can finish in y days, C and A can finish in z days, then
Formula 9:
If A is k times more efficient than B and so able to finish the work in l days then,
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