Aptitude - Time and Work - Discussion

Given
A completes 80% work in 20 days (20% work in 5 days).

A alone can complete 100% work in 25days(20/80*100=25)
A+B together complete 20% of the work in 3 days
A+B together complete 100% of the work in 15 days.
Here we need to consider only 100% work done by A+B&A.
(A+B)-A = [1/15 - 1/25].
LCM of 15, 25 is 75.
(A+B)-A = [5-3]/75,
(A+B)-A = 2/75,
(A+B)-A = 37.5.

A completes 80% of the work in 20 days.
This means A does 4% of the work each day (80% ÷ 20 days).
In 3 days, A would complete 12% of the work (4% × 3 days).
The remaining work, 8%, is done by B in 3 days.

To find out how long B would take to complete the entire work (100%), we calculate it as follows:

If B does 8% of the work in 3 days, then B's work rate is 8% ÷ 3 days = 2.67% per day.
Therefore, to complete 100% of the work, B would require:
100% ÷ 2.67% per day = 37.5 days.
So, B would take 37.5 days to complete 100% of the work.

Work done by A in 20 days = 80/100 = 8/10 = 4/5.
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --> (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because the remaining 20% is done in 3 days by A and B).
Work done by A and B in 1 day = 1/15 --> (2).
Work done by B in 1 day = 1/15 " 1/25 = 2/75.
=> B can complete the work in 75/2 days = 37 (1/2) days.

80% of the work in 20 days means 4/5.
100% he will complete in 25 days.
Now, the remaining 20% of the work in 3days means;
1-4/5 = 1/5 this is for one day
For 3days 3*1/5 = 1/15,
Now [1/15 - 1/25] = 2/75.
Rev= 75/2=37.5

@All.

Here A do 80% work in 20 days.

That mean remaining work = 20%.
On diving 80 by 20 = A do 4% work in 1 day
So the remaining 20 % has to be done in 20/4 =5 day.

Now, total days were taken by A = 20 + 5 = 25.
Now, ACC to question;

A+B Takes 3 days to complete the remaining work so 5 * 3 = 15 days.
Now;
A= 25,
A+B=15.

On taking LCM we get 75.
So now by dividing,
A's efficiency = 75/25 = 3,
A+B efficiency= 75/15=5.

Now B efficiency = 5-3 = 2 bcz A+ B= 5 nd A=3.
Now dividing B efficiency from total working days = 75/2 = 37.5.

(no of days required A to complete 100% work + no of days required B to complete 100% work) * no of days
= no of days required complete whole work by A+B -----> 1
A per-day work = 20/80 = 1/ 4 meaning 4 units/day.

Hence, no of days required A to complete 100% work = 100/4 = 25 days.
No of days are required to complete the whole work by A+B = 100/20 = 5.
The sub in 1.
(1/25 +1/B) *3 = 1/5.
3/B = 2/25.
B = 25*3/2
B = 37.5

A -> 80% work in 20 days.
A + B ---> 20% work in 3 days.

A --> 100% work in 25 days.
A+B ->100%work in 15 days
LCM of 25 and 15 is 75.
Capacity of A is -->3 units
Capacity of A+B ---> 5 units.

So, the total work was 75(LCM).
B capacity = A+B (Capacity)-A(capacity).
B(Capacity) = 5-3.
B(Capacity) = 2.
B(work) = totalWork/B(Capacity).
B(Work) = 75/2.
B(Work) = 37.5.

A can do 80% of work in 20 days.
A + B 20% of work in 3 days.
A alone can do 20% of work in 5 days and A+B can do 80% in 12 days.

Now, A 100% in 25 days and A + B in 15 days.
L.C.M of 15 and 25 = 75
The efficiency of A is 3/day and of A + B 5/day.
If A efficiency is 3, then B is 2.
B days = work/B efficiency.
=> 75/2 = 37.5.

A's 80%=20days.

So we want 100% of A's Work
Therefore
A*(80/100) =20
A*(4/5) =20
A =(20*5) /4
A =100/4=25
So A's 100% of work finished in 25 days. Therefore A=1/25 ...... (1)

Now remaining (100,.-80%) =20% work done by (A+B) in 3 days

(A+B) 's 20%=3days

So we want 100% of (A+B) 's work

(A+B) *(20/100) =3
(A+B) *(1/5) =3
(A+B) =3*5
=15 days

so (A+B) finished in 15 days
therefore
(A+B) =1/15...........(2)

From equation (1) & (2)
(A+B) =1/15
(1/25) +B=1/15 [A=1/25]
B=[1/15]-[1/25]
B=[5-3]/75 [75/15=5 & 75/25=3]
B=75/2
B=37(1/2) days [remain 1/2]

So do it in notebook otherwise you can't understand.
Take the left side of the notebook & derive A's 100% of work and right side of the notebook derive (A+B) 's 100% of work.

Then the middle side of the notebook solves these A's and (A+B)'s. You get B's 100% of work. that is the answer.

now check it
(1/25) +(2/75) =1/15

5/75=1/15 [(75/25) =3 & (75/75)=1]
1/15=1/15.
LHS=RHS.

Thanks.

Thanks @Karan.