Aptitude - Time and Work - Discussion

Good, Thanks @Keerthan G.

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.

Finally, I understood the concept, Thanks @Rajendra.

@Rajendra.

Thank you for explaining.

This can also be solved in this way.
A - 80% work in 20 days .
=>1/A=1/20 (1 day work of A) ---> 1

Also Given remaining 20% work done in 3 days by help of B.
Let us calculate days if they work for other 80%.

20% = 3 days.
80% = x.
x = 12 days.
=> 1/A + 1/B = 1/12.

Substitute value of 1/A from eq 1
then B = 30

=> 80% = 30 days,
100% = x.
By calculating x = 37.5.
So, B alone can finish work in 37.5 days.

Sorry I can't get it why we should multiply with that 5/4 ?

A does 80% in 20 days..so
A does 100% in 25 days..
A's 1 day work=1/25
A+B does 20% in 3 days..so
A+B does 100% in 15 days
A+B's 1 day work=1/15
1/25+B=1/15
B=1/15-1/25
B,s 1 day work=2/75
so B,s work=75/2 i.e 37 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.

@Baskar.

Thank you very much for your explanation.

@shefali..the 15 days is nothing but remaining work probability. 4/5 i.e 80% work is done by A so remaining is 1-(4/5)= 1/5. its same like p+q=1 in probability.
n same like 3*5=15 days