Aptitude - Time and Work - Discussion

Thanks for the explanation @Baskar.

80/100 is 4/5 then how you get it as (20*5/4) =25?

How 1-4/5? Please explain it.

3(A+B)20%. = 80%(20A),
3/20*100. = 20/80*100A
15days(a+b). = 25 days A alone
B alone work = 1/25-1/15 = 2/75; 75/2.

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.

A complete 80 work on 20 day then efficiency is 4.
A & B complete remaining 20 work in 3 days.
So A works 4*3=12 in 3 days.
12+80=92.
and B complete 8 works in 3 days.
and efficiency of B is 8/3.

Hence B will complete whole work in 100/(8/3) = 75/2.

Nice method, Thanks @Suganya.

Good explanation, thank you @Rajendra.

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 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.

20 days-80% => 1 day-4%.

In 3 days a+b-20% => 3b=20-3*4% = 8%.

b = 8/3% => 100*8/3 = 37.5.