Aptitude - Time and Work - Discussion

80% in 20days.

100% in ? ==>25 days.
A's work per day = 1/25,
A completes 80% of work = remaining 20% of work = 20/100 of 1 = 1/5.

Together they complete in 3 days.
(1/25 + 1/B) *3= 1/5
SOLVE:
1/B = 2/75 = B's work per day.
For B to complete = 75/2 = Answer.

A:
80% in 20 days then
100% in x days
Cross multiply them you will get 25days

A+B:

20% in 3 days then
100% in y days
Cross multiply them you will get y=15.
Now: A's one day work is 1/25.
& A+B's one-day work is 1/15.

A+B one day work minus A one day work =1/15 - 1/25 = 75/2.

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.

@Baskar.

Thank you very much for your explanation.

Your explanation is short and good.

Thanks @Ajith.

Hey Guys! Let's view this differently,

|80% = 80/100 = 4/5|
|20% = 20/100 = 1/5|

As/Q,
4/5 A = 20 => A = 25 --> 3 <-- Efficiency of A {as, TW/25=3}
LCM (25, 15) = 75 <-- Total Work, TW(say).

1/5 (A+B) = 3 => (A+B) = 15 --> 5 <-- Efficiency of A+B {as, TW/5=5}.

Since the Efficiency of A is 3 and A+B is 5, this implies, the efficiency of B is 2.

Now,
TW=75 and B's efficiency is 2,
So, no. of days needed by B is, 75/2 = 35.5 <--answer.

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.

A finish 80% work in 20 days.
A finish 100% work in 20/80*100 = 25 days,
A+B finish the remaining 20% of work in 3 days,
A+B finish 100% work in 3/20*100 = 15 days.

Now A finishes the whole work in 25 days and A+B finishes the same work in 25 days.
Now total work is LCM of 15 and 25 =75

A's work of one day =75/25 = 3.
A+B work of one day=75/15 = 5.
B's work of one day= (A+B)-A = 2 - 3 = 2.

Now the time is taken by B to complete the whole work= total work/B's per day work =75/2 = 37.5.

Here;
20 is 80 %,
25 is 100%,
A+B = 3 days this is 20 %.
20% * 5 = 3 * 5 for 100% work,
B= A+B- A.
B=1/15- 1/25,
B = 2/ 75 = 37.5.

A=80%
Remain 100 - 80 = 20%.

A = (1/20) * (80/100) = 1/25.
A+b = (1/3)+(20/100) = 1/15.
A+b.
(1/25) + b = 1/15.
B = 2/75,
B = 75/2,
B = 37(1/2).