Aptitude - Time and Work - Discussion

Very simple,

A's 1 day work = (0.8/20).
(a+b)'s 1 day work = (0.2/3).

So, b's work = (0.2/3) - (0.8/20).
= 2/75.

Therefore days taken by B = 75/2 = 37 1/2.

Thank you @Vishnu.

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.

Thank you @Bhaskar.

A alone completes the work in 25 days.
A and B together can complete the work in 15 days.
Let the total work be 75 units(LCM of 15 and 25).
i.e., A= 3 units /day ; A+B=5 units/day.
i.e.,B can do 2 units/day.
=> B alone can do the work in 75/2 days.

@Swapraj.

This is how it goes,

A---> 80% work--->20 days.
100% work---> How many days (say 'X' days).

Then you cross multiply it and you get the solution.

80%= 4/5.

But, work done by A = 5/4 * 20 why not 4/5 * 20.

Please explain me.

A can do 80% of work in 20 days which means that he can do 100% work in 25 days.
A and B together can do 20% work in 3 days which means that they can do 100% work in 15 days.

Now,A's 1 day work=1/25--------->1/A=1/25.
(A+B)'s 1 day work=1/15------> (1/A)+(1/B)=1/15.
From the above two equations,(1/25)+(1/B)=1/15 which gives 1/B=2/75.
-->B=75/2=37.5.

Easy to understand it. Thanks @Wilson.

A does 80% work means 80÷100 =4/5 work in 20 days.
So, A's 1 day work = 4/5 * 1/20 = 1/25 work in 1day.
Now, It is said that A+B can do a piece of work in 3 days.
Therefore remaining work =1 - 4/5 = 1/5.
So, A+B's 1day work = 1/5 * 1/3 = 1/15.
Now work done by B in 1 day = 1/15-1/25 = 2/75.
Therefore B can do whole work in 75/2.

Hope it is clear to you!