Time and work question

Question

three persons a ,b and c decide to work in such a way that a and c work together on 1st day ,b alone on 2 nd day , a and c on 3 rd and so on on alternate days .how many days will be required to complete the whole work if c and d alone finished the whole work in 20 days and 34 days respectively and b is 70% more efficient than D but 20 % less efficent than A

Answer 1

c=20

d=34

b=0.7 * 34 = 23.8

a=1.2 * 23.8 = 28.56

The first team (A and C) do the work like so:

1/28.56 + 1/20

the second team (B) does the work like so:

1/23.8

[To understand the foregoing, consider the following:

party Q does 1/2 the work in one day

it takes party Q 2 days to do 2/2, or all, of the work.]

So, day one, again looks like the following:

0.085 of the work gets done

day two looks like the following:

0.042 of the work gets done

adding the two days together, we see that in two days, 0.127 of the work gets done.

So divide 1/0.127, and we see the number of pairs of days it takes to get the work done.

That number is 7.874

Multiply that figure by two to see the number of total days on the job:

15.75

It is easier, perhaps, to look at the fractions, or the decimals in terms of percentages.

For example, if 8.5% of the work gets done in day 1, and in day 2, 4.2% of the work gets done, together, they are about 12.7% of the work done each two days.  

divide 100% of the work by the two-day percentage of 12.7% and you get 7.874, which needs to be multiplied by two, since the question asks for days and not pairs-of-days, so it’s, again, 15.75 days.