Aptitude - Time and Work - Discussion

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.

We have to find how many days B alone can complete the entire job.
80% of work by A in 20 days.
100% of work done by A ? days .

(100*20)/80= 25.

In the actual explanation instead of 80% they have take fraction 80/100 =4/5 and 100% =1.
4/5 work in 20days.
1 work in ? days .
so it is (20*1)/ (5/4) = 20*(5/4) =25.

25 days taken by A to complete entire 100%work .(why we convert to 100% work done by A is because we need it"s one day of work which is 1/25 not 1/20)

Now keep ready A's 1day of work which is 1/25.

20% of work done by A and B -- 3 days.
20% is nothing but 20/100 = 1/5.

20% of work done by A and B in 3 days.
100% of work " " A and B in ? days
100*3/ 20 = 15 days,
A+B = 15 days,
Now calculate 1 day of work of B.

1/25 + B's 1 day work = 1/15
B's 1-day work = 1/15 - 1/25 = 2/75 1 day of work by B is 2/75 and entire work in 75/2 days. If you ask why inverse check A's 1 day of work and entire work ( 1/25 one day work, inverse 25days complete work).

Hope this helps to better understanding.

==>> A can do 80% W ---------> 20 days.

=> Then, 100% W ---------->

=> How many days(D), By Cross-multiplying we get,

D = (100*20)/80 ==> D = 25.

i.e., A can do 100% of the work in 25 days.

So, A's 1 day work, i.e., 1/A = 1/25 -----------------------(1)

The remaining work is 20%.

==>> Given A+B can do the 20% W --------> 3 days.

=> Then, 100% W ------------------------>

=> How many days(D), By cross-multiplying we get,

D = (100*3)/20 ==> D=15.

i.e., A+B can do 100% of work in 15 days.

So, A & B one day work i.e., 1/A + 1/B = 1/15 -----(2)

Solving 1 & 2, we get B's 1-day work as 1/B = 2/75.

So,

B alone would take to do the whole work i.e., B = 75/2 = 37(1/2) days.

For all friends..
work = days

for A:
80% work = 20 days
4/5 work = 20 days
cross mul
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 mul
1 work = 15 days
dat is

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 mul
B's work = 75/2 days = 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.

Here the answer in simple steps:

A 's work in 20 days = 80/100 = 4/5

Then, A's 1 day work is = 4/5*20 =4/100=1/25.

(Here we simply multiply the 20 in the denominator)

So,

A+B 's 3 days work = 1/5
A+B's 1 day work = 1/5 * 3 = 1/15.

(Here the 1/5 comes as, in Factional total work is 1 so when we subtract the A s 4/5 from 1 we get the remaining work which is going to complete by A and B is 1/5).

So we got A's work and A+B 's work when we subtract the both we got B's time to complete it
1/15-1/25 = 2/75 it is an efficiency when you reciprocal it, we got 75/3 that is in 35.5 or 35 1/2 days.

For A
Here 80% work is done by A in 20 days.
so 80/20 = 4% work per day.
So,remaining 20% will take 20/4= 5 days.
so A will take 20+5= 25 days to complete 100% of work.
so A's 1 day work is 1/25 --------------(1)


---------------------------------------------------------
Similarly, remaining 20% is done by both (A & B) in 3 days.
so (20/3)% work per day.
Now, 100% work will be completed in 100/(20/3)
i.e. 100 x 3/20 =15 days.
(A + B)'s one day work is 1/15.
So,
A + B = 1/15
1/25 + B = 1/15
B = 1/15 - 1/25
SO B's one day work = 4/150 = 2/75
So B will take 75/2 days. i.e. 37 1/2 days.

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.

80% work done by A -------->20 days (given)
1 work ie. 100% work done by A ------->20*100/80 = 25 days
therefore, total work is done by A = 25 days

Now,
20% work done by (A+B) implies,

20/100 work done --------> 3 days.
1 work ie. 100% work done in ------>3*100/20.= 15 days.

Now we have,
A's 1 days work = 1/25 ----------------------> 1
and, (A+B)'s 1 days work = 1/15 -------------------------> 2

Putting A's work in equation 2.
B's one day work = 2/75.

Therefrom total work done by B = 75/2.
= 37 1/2.

Hi Guys,

General Concept: Time and work

A can complete work in X days
1.e., A can complete 100% of work in X Days

A's 1 day work = (Amount of work completed) /(number of days)
so,
A's 1 day work = 100%/X => 100%(1/X)

Now,

A completed 80% of work in 20 Days
so, A's 1 day work = 80%/20 => 1/25

A+B completed 20% of work in 3 days
so, (A+B)'s 1 days work = 20%/3 => 1/15

A+B = 1/15
B = (1/15-1/25) => 10/375

B's 1 day work = 100%/(10/375) => 100%(375/10)

B alone completed 100% of work in 375/10 Days

B = 37.5 Days => 37 1/2 Days