12 men can finish a project in 20 days. 18 women can finish the same

Let's assume the total work to be done is 720 units (LCM of 20, 16, 18).

Now, men put together complete the work in 20 days and their combined efficiency is 720/20 = 36 units/day.
Therefore, efficiency of 1 man = 36 units/12 men = 3 units/day

Similarly if we do for women and children, we get:
Combined efficiency of women = 720 units/16 women = 45 units/day and efficiency of 1 woman = 45/18 units per day
Combined efficiency of children = 720 units/18 children = 40 units/day and efficiency of 1 child = 40/24 units per day.

Since it is given that 8 women and 16 children worked for 9 days, we can calculate the total units of work done by them:

(45/18)*8 women*9 days + (40/24)*16 children*9 days = 420 units

The pending work of 300 units (720-420) is done by 10 men. The efficiency of 10 men is 30 units per day (3 units/day *10 men).

Therefore, 300 units of work can be completed by 10 men in 300/30 = 10 days.

I'm confused how total work has been calculated 12 x 18 x 20
Can someone guide for this part

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SantoshSukumaran

Substitute the value of \(m\) or \(w\) or \(c\) at any of the below equation to calculate the total work;
\(12m∗20=18w∗16=24c∗18 \)
It is always equal in all cases. Hope this clarifies your query.
Cheers meanup!

It took me 4 minutes with direct calc. can anyone suggest any shortcut for these type of questions?

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Took a while to figure out a solution.
I worked with the work formula
Men×days×hours = work

1.for Children - 24×18/1 = 16 ×9 / W2. I am considering total work to be 1 .
W2 is work done by 16 CHILDREN for 9 days.

W2= 1/3 .

2.for women - 18 × 16/1 = 8 × 9/w3

W3 is work done by 8 women in 9 days.
W3= 1/4.

W2 + w3 = 1/3 +1/4 = 7/12.

So remaining work left for the men to finish is = total work - 7/12, i.e 1- 7/12=5/12.

Now we knw that 12men take 20days to finish complete work , hence equating this

12 ×20/1 = 10 × D / (5/12)

On solving we get D = 10days.

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Total days required for job to be done:

1. Man - 240 (12*20)
2. Women - 288 (18*16)
3. Boys - 432 (24*18)

We equate them since, it pertains to one job. We get 5 men days = 6 women days = 9 boy days
Now, work done by women and men for 9 days is:

8 Women - 72 woman days => 60 man days
16 Boys - 144 boy days => 80 man days

Balance hours remaining is 100 man days (=240-140), which can be done by 10 men in 10 days.