Time and Work:Problem on More People

Question: Twenty four men can complete a work in sixteen days.Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started working and worked for twelve days.How many more men are to be added to complete the remaining work in 2days?

Solution:

As per concept,
If(a person) finish the work in “n days” .
Then(a person 1day work )=[1/n],

If(24 men)finish the work in”16 days”
Then 24men 1 day work =1/16

From above find it for by (1man 1 day work),

24men 1 day work =1/16
Also we can write (24*1)men 1 day work=1/16
(1man 1 day work)= 1/(16*24)
(1man 1 day work)= 1/384
Therefore, Workdone by 1man in 1 day =1/384
---------------------------------------------------------------------------------------------------------------

Similarly ,
We can find Workdone by 1woman in 1 day work 

Given that Workdone by 32 woman in 24days
As per concept,
If(a person) finish the work in “n days” .
Then(a person 1day work )=[1/n],

If(32 women)finish the work in”24 days”
Then 32 women 1 day work =1/24

From above find it for by (1woman 1 day work),

32women 1 day work =1/24
Also we can write ,
(32*1)women 1 day work=1/24
(1woman 1 day work)=1/(24*32)
(1woman 1 day work)=1/768
---------------------------------------------------------------------------------------------------------------

Find the remaining work and No.of men in 2days for remaining work :

Given that, Sixteen men and sixteen women started working and worked for twelve days.How many more men are to be added to complete the remaining work in 2days?

So,First we have to find the remaining work.
Second we have to find how many men needed to finish remaining work in 2 days

Find work done by 16 men and 16 women for 12 days
Then 16 men and 16 women 12 day work[and means +]
W=(16 men + 16 women ) 12 day work
W=(16 *1man + 16*1 woman ) 1 2*1day work
W=16*12[1man1day work+1 woman 1day work]
W=16*12[(1/384)+(1/768)]
W=16*12[3/768]
W=3/4
Remaining work=1-(3/4)
Remaining work=1/4
---------------------------------------------------------------------------------------------------------------
This remaining work 1/4 need to be finished in 2 days by adding more men with16 men and 16 women .
So,calculate 2 days work of 16 men and 16
W=(16 men + 16 women ) 2 day work
W=(16 *1man + 16*1 woman ) 2*1day work
W=16*2[3/768]
W=3/24
W=1/8
The remaining work need to to be finished in two days,
W=1/4-1/8
W=1/8
(1man 1 day work)= 1/384
384 men able to complete 1 work in 1 day.
For 1/8 work------>384/8=48
48 men able to complete 1/8 work in 1 day.
For 2 days--------->48/2=24
Therefore 24 men are required to finish the work.