Aptitude - Time and Work - Discussion

Whole work done by A is?

In 20 days 80%
In how many days 100%
80% in 20 days.

100% in x days ---- cross multiply.
100 * 20/80 = 25 days.
A completes work in 25 days.

Now A+B
20% in 3 days
100% in x days ---- cross multiply.

100 * 3/20= 15 days.
A+B complete work in 15 days.
now A's one-day work = 1/25.
A+B one day's work = 1/15.
now we want B,
B=(A+B)-A,
=(1/15)-(1/25)=>2/75............................B's one day's work,

Work done by B is (reciprocal of B's one day work) 75/2 days

now divide 75/2.

75/2=37 and the remainder is 1.
hence answer is 37*(1/2)days.

For A:
80% work = 20 days.
4/5 work = 20 days.
cross multiply.
1 work = 5/4 * 20 days.
1 work = 25 days.
A's 25 days = 1 work ------>1.

A+B remain work done in 3 days.
total work = 1,
80% work = 4/5,
100% work = 1,
100% - 80% = 1 - 4/5 = 1/5.

For A+B:
Work = days.
1/5 work = 3 days.
Cross multiply
1 work = 15 days.


And A+B's 15 days = 1 work ---->2

Now we know A's and A+B's work
Now find B's work
Apply A's in A+B's.

A+B 1 Days= 1/15 works
A's 1 days = 1/25 works---->from 1..

1/25 + B = 1/15 works.
B's days = 1/15 - 1/25 Works.
B's days= 2/75 works.
we have to calc works.
cross multiply.
B's work = 75/2 days = 37 1/2 days.

Please, anyone, help me to get it clearly.

80% = (80/100).

so, A's (80/100) work done in 20 days.

Total Work of A = (100/80 * 20) = 25 //
Now if we consider total Work as 1.
4/5 part was already done by A remaining 1/5 he completed with the help of B.

So, (1/5) of work done by (A+B) in 3 days,
by calculating we get (A+B) = 3*(5/1) = 15 days,

Now to find B's Work we have A+B=15.
substitute A value and in above equation i.e (A+B = 15).

so
1/25 + 1/B = 1/15.
1/B = (1/15) - (1/25) ---- (LCM = 75).
1/B = (5-3) / 75,
1/B = 2/75,
B = 75 / 2 = 37 1/2.

Thank you @Baskar.

Thank you @Rajendra.

A do 80%work for 20days.

(Simplify it remaining 20%do in 5days).

Now work for 20%is 1/5 and work are done by both a+b is 1/3. Do lcm we get 15 and subtract 5-3/15=2/15.
Now it is 20% of work done by B is 2/15.
Now 20%*5=100% i.e,2/15*5=2/75 ans is 37 1/2 days.

Thank you so much @Baskar.

Thanks @Ganesh.

Let's take 5 parts total.
A finishes 80% of it in 20 days, A can finish whole work in 25 days.
A one day work is 1/25.
A= 4/5 work in 20 days.
Remaining, 1-(4/5)= 1/5 part.
(A+B)= 1/5 work in 3 days.
A's 3 days work = 3/25.
Therefore,
For 3 days, A+B= 1/5.
(3/25)+B= 1/5.
B= 2/25 in 3 days.
B's one day work, 2/75 work.
Whole work by B= 75/2.
B = 37 1/2 days.