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Time & Work

Formulae :
Work And Time :
We assume that total work is unit
If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
If A and B work together for n days, then (A+B)’s 1 day’s work = 1/n
If A is n times efficient than B, then
A’s one day work = n( B’s one day work()
eg: If A is twice as good workman as B, the ratio of work done by A and B= 2:1.

Wages :
Wages are indirectly proportional to the time taken by the individual.
Wages are directly proportional to the work done.mean more money for more work and less money for less work.

For Example- 4 men and 6 women working together can complete the work
within 10 days. 3 men and 7 women working together will complete the same
work within 8 days. In how many days 10 women will complete this work ?

Explanation : Let number of men =x, number of women = y
⇒ Efficiency of 4 men and 6 women = 100/10 = 10%
         ⇒ so, 4x+6y = 10
Above equation means 4 men and 6 women can do 10% of a the job in one day.
⇒ Efficiency of 3 men and 7 women = 100/8 = 12.5%
          so, 3x+7y = 12.5
By solving both equations we get, x = -0.5 and y = 2
⇒ Efficiency of 1 woman(y) = 2% per day
⇒ Efficiency of 10 women per day = 20%
So 10 women can complete the job in 100/20 = 5 days