Aptitude - Time and Work - Discussion

Let A's 1 day's work = x and B's 1 day's work = y.
Both A's and B's 1 day work=1/30
i.e (A's 1 day + B's 1 day)=1/30
i.e x + y = 1/30........eq1
now,
A having worked for 16 days, B finishes the remaining work alone in 44 days
i.e work done by A in 16 days = 16x
Remaining work done B= 1 - 16x
but Remaining work is done by B in 44days i.e 44y
i.e. 44y=1-16x
i.e 16x+44y=1........eq2
solving eq1 & eq2,
we get,x = 1/60 and y = 1/60
B's 1 day's work = 1/60.
Hence, B alone shall finish the whole work in 60 days.

Selvi. You are wrong absolutely.

How can we write 16x+44y=1. I cant understand.

Can anyone tell how to solve efficiency questions of time & work?

Like.

A is 140% efficient than B. B starts the work & does 5 days then A completes the remaining work in 10 days. In how many days does A take to complete the same work.

Please, anyone tell me.

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.

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.

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.

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.

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?

Can somebody solve it in the shortcut?