Aptitude - Time and Work - Discussion

Here's a simple explanation :

WORK = (Rate)*(Time) ***time will cancel out***

First Day: Person A does all the work.

His working rate is 1/20 so (1/20)*1day = 1/20 work.

Second Day: Person A does all the work.

His working rate is 1/20 so (1/20)*1day = 1/20 work.

All in all in 2 days is 2/20 or 1/10.

Third Day: Person A is assisted by B and C.

(1/20)+(1/30)+(1/60) times 1 day = 1/10.

All in all in 3 days is (1/10)+(1/10)= 1/5 work is done.

So 4/5 remaining..

Question Says B and C assisted A EVERY third day.

Repeat the process until you get 5/5 or 1 full work that would be on the 15th day, A will complete 5/5 or 1 full work.

Why we taken 1/10+1/10?

@Divya.

First Two days work done by A = (1/20)+(1/20)=> 2/20=> 1/10.

Third day work done by A,B,C = (1/20)+(1/30)+(1/60)=> 6/60 => 1/10.

Total work Done in 3 days= (1/10)+(1/10)=2/10 =>1/5.

Let N be the total no.of days A has to work. So, a/q B and C works only for N/3 days. Total work = 1.

Therefore,

N*(1/20)+ (N/3)*((1/30)+(1/60)) = 1.

Solving this , you will get N = 15.

First Two days work done by A = (1/20)+(1/20)=> 2/20=> 1/10.

Third day work done by A, B, C = (1/20)+(1/30)+(1/60)=> 6/60 => 1/10.
3 days work done: 1/5.

Then 1 day work done: (1/5)*(1/3) = 1/15.

So the answer is 115 days.

A's 2 day's work = (1/20x2) = 1/10.

(A + B + C)'s 1 day's work = [(1/20)+(1/30)+(1/60)] = 6/60 = 1/10.

Work done in 3 days = [(1/10)+(1/10)] = 1/5.

Now what they ask "How many days can "A" do the work?"

Here revise the FORMULA NO:2.

That is:

Days from Work:

If A's 1 day's work =1/n,then A can finish the work in n days.

Here ===> [1 DAY's work = NO.of WORK / required "n" Day's do the work ].

We want no.of DAY's;

So rearrange the formula; we get,

No.of WORK = (1DAY's work * "n" DAY's) ------> take eqn no.1.

Now, (1/5) work is done in 3 days.

3 = 1/5.

So apply above the data's in eqn no.1.

1(No.of Work) = (Day's of Work )3 * ("n" DAY's)5.

1(No.of Work) = 15 Day's

So "A" is require 15 Day's to do a 1 work.

"I HOPE U WILL B UNDERSTAND"

I didn't get step 1 how a 2 days work? I mean why we multiply with 2?

Guys, as per my understanding,

1st day A complete 1/20th of work.

2nd day A completes 2/20th of work.

3rd day A along with B and C completes (3/20+1/30+1/60) i.e., 1/5th of the work.

Could some one explain how to calculate?

4th day of A's work ?

5th day of A's work?

6th day of A along with B and C ?

It would be better if it is done in this way.

B, C assist A on the 3rd day so directly we get,

3/20(3 day's of A) + 1/30(assistance of B) + 1/60(assistance of C) = 1/5.

So 1/5 done in 3 days whole is done in 15 days.

1/5 of work --->3 days.

1 complete work ---> ?

= (1*3)/(1/5).

= 15 days.