Aptitude - Time and Work - Discussion

A+B do whole work in 30 days(100% of work or Complete).
A+B's1 day work =1/30.
Let us take assumption as usual.
A's 1 day work = x , & B's 1 day work = y.
=> x+y=1/30 ------------ eq1.
Now people got confused by;

This 16x +44y =1.
(Ans. It is equal to 1 coz 1 here means 100% or mathematically 1/1=1 and in eq1 1/30 means 1/30 100%work--1 divided into 30 parts has been done in 1 day 1/30%=3.3%).
And simply 1 means 100%. 1/1*%. Or 1/1x100.

a+b = can do a work in 30 days.
A work for 16 day means 14 days work left.
B do the work for 44 days means extra 14-day work from 30-day timeline.

That is 14. a = 14.b (14day work left is don by b in extra 14-day work).
a/b = 1/1.
Total work = 30.(1+1)= 60 ( 30 days and both efficiency).
B alone can do= total work/b efficiency= 60/1.
60 is the answer.

2 workers A + B together could finish a work in 8 days they work together for 6 days & A left the works the remaining works was completed by B alone in 6 days. How many days would each take to complete the individual?

How to solve this problem?

1/30 - 1/16 = 7/240

2*1 / 44 = 1/22

7/240 - 1/22 = 43/2640

Guys this is very very simple.

Time taken by A + B : 30 days.
They didn't mention the efficiency of neither A nor B.
So we can take 50/50 efficiency.
For example
Total: 30 candles.
A+B making 30 candles in 30 days.

So, A alone makes 30 candles in 60 Days.

Can somebody solve it in the shortcut?

1 represents whole work..i.e
16X + 44Y =1
Means A having work for 16 days and B remaining in 44 so whole work is represented by 1 always.

Supplementary argument.
Like wise if A work 4/15 ( 16/60) and B remaining work 11 /15 ( 1- 4/15) which is done in 44 days.

4 / 15 + 11/15= 1 makes whole work.
Here we write X for A because we don't know As whole work alone and similarly Y for B too. The only thing we know is the remaining work.

Hope understand better now.

Let work done by A in 1 day be a and the work done by B in 1 day be;

A and B together can do a piece of work in 30 days.
=> Work done by A and B in 1 day = 1/30.
a + b = 1/30...........(1),

Work done by A in 16 days + work done by B in 44 days = 1.
16a + 44b = 1 ...........(2).

Solve (1) and (2)

Multiply equation (1) with 16 => 16a + 16b = 16/30=8/15 .......(3)
Subtract equation (3) from (2) => 28b = 1 - 8/15=7/15,
b = 7/15 * 1/28=1/60.

i.e., B alone needs 60 days to finish the work.

Consider like this,

A and b completes a work in 30days. So this means both individually work for 30 days. Let us assume they do some bottles. If 60 bottles they have to do. It can be 30 bottles each or it can be 45 and 15 bottles or 40 & 20. So it depends upon each one capability.

So we can frame an equation like this,

30x+30y=1 (where x and why are the number of bottles per day. It is equated to 1 because for a day we are calculating).

Similarly, if A works for 16 days and B work for the 44 days,

So it will be 16x+44y = 1.

Solving and we will arrive at the answer.

My method:- Mixture

A -------------- B
16 -------------- 44
30 --------------
14 : 14
1 : 1

So, B completed the whole work( means A's work +B's work alone)=(16 x1 +44 x 1) = 60 days.