Time & Work 3

1. If A completes a work in x days and B in y days then ratio of works done by in 1 day will be y : x.

2. If A does twice of the work done by B, then the ratio between the works done by A and B will be 2 : 1

If the number of days to complete the work is less, then the number of people required to complete the work will be more. In other words the ratio in which the number of people will increase, the number of days decreased will be in the ratio. For example, if 5 people complete a work in 4 days, then number of days required by 1 person to complete will be 4 × 5 = 20 

Example 1. 16 boys take 12 days to complete a work while 12 men do the same work in 8 days will be the remaining work is completed?

Solution : 

16 boys do in 12 days 1 work

1 boy will do in 1 day = 1 / (16 x 12)  = 1 / 192

Similarly 1 man will do in 1 day = 1 / (12 x 8 ) = 1/96

work of 1 boy / work of 1 man  =  (1/192) / (1/96) = 1/2

Or, Work of 2 boys = Work of 1 man

(16 - 6) men + 4 boys = 10 men + 2 men = 12 men

And work done by 16 men in 3 days =(1/96) x 16 x 3 = 1/2

Remaining work = 1 - (1/2) =1/2

Therefore 12 man do 1 work in 8 days

12 man do 1/2 work  (8 x 12 x 1) / (12 x 2) = 4 days

Exercise Problems:

Example 2. If 3 men can work as much as 4 women then what is the ratio of work done by 1 man and 1 woman?

Example 3: A can complete a work in 30 days while B can complete the same work in 40 days. If they work together, then in how many days will they complete the work?

Example 4: If Manohar can reap a field in 6 days while Manohar and Davendra together can reap the same field in 4 days. In how many days will Davendra alone reap the field?

Example 5: Shyam can build a wall in 12 days, Babulal in 15 days and Kishori in 18 days. In how many will the wall be built if they all the three work together?

Example 6: 10 men can complete a work in 10 days while 12 women in 20 days. In how many days will 15 men and 6 women together complete?