Time and Work - Quiz

If A and B can dig the trench in 12 days, then their combined daily rate of progress is 1/12 of the trench per day.
Similarly, if A can dig the trench in 30 days, then his daily rate of progress is 1/30 of the trench per day.
Therefore, B's daily rate of progress is 1/12 - 1/30, which simplifies to 1/20.
So, it would take B alone 20 days to dig the trench.

If A can complete a task in 25 days,
and B can complete the same task in 20 days, then their combined daily rate of progress is 1/25 + 1/20 of the task per day.
Therefore, their 5 days of work together represents 5 * (1/25 + 1/20) = 9/20 of the task.
This means that the remaining work to be done is 1 - 9/20 = 11/20 of the task.
If B can complete 1/20 of the task in one day, then it will take him 11 days to complete the remaining 11/20 of the task

The proportion of A's and B's shares can be calculated by comparing the time it takes them to build the wall individually.
In this case,
A can build the wall in 30 days and B can build it in 40 days,
so the proportion of their shares is 4:3.
Using this proportion,
we can calculate B's share of the payment.
In this case, B's share is RS. 3000.

If A and B are able to complete a task in 3 days when working together,
and they start the task together,
but B leaves after 2 days and the task is completed 2 days later,
it would take B alone 6 days to complete the task.

If the work rate of A is 1/x of the task per day,
the work rate of B is 1/x of the task per day, and the work rate of C is 1/x of the task per day,
then the combined work rate of A, B, and C is
(1/x + 1/x + 1/x) of the task per day, which is equal to 1/2 of the task per day.
Therefore, x = 12, which means that B takes 6 days to complete the task on their own

If B and C can complete 1/36 of the work per day together,
and they work for 3 days before leaving, then the remaining work is 5/12 of the task.
Since A can complete 1/24 of the work per day,
it will take A 10 days to finish the remaining work

The work can be completed by A and B in 18 days, so the amount of work they complete in 1 day is (1/18) of the total work.

The work can be completed by B and C in 24 days, so the amount of work they complete in 1 day is (1/24) of the total work.

The work can be completed by A and C in 36 days, so the amount of work they complete in 1 day is (1/36) of the total work.

The amount of work A, B, and C complete in 1 day is the sum of the work completed by each pair in 1 day. This is (1/18) + (1/24) + (1/36) = 9/72 = 1/8 of the total work.

Since A, B, and C complete (1/16) of the total work in 1 day, it will take them 16 days to complete the entire work. 

A is twice as good a workman as B, so the ratio of A's work to B's work is 2 : 1.

A and B can finish the work in 18 days, 

so the amount of work they complete in 1 day is (1/18) of the total work.

We can divide the amount of work they complete in 1 day in the ratio 2 : 1, 

with A completing 2/3 and B completing 1/3.

Therefore, A's 1 day's work is (1/18) * (2/3) = 1/27 of the total work.

Since A completes (1/27) of the total work in 1 day, it will take him 27 days to complete the entire work.

B is 60% more efficient than A, 

so the ratio of the time it takes B to complete the job to the time it takes A to complete the job is 

100% + 60% = 160% : 100%. 

This can also be written as 8 : 5.

Let's suppose it takes B alone x days to complete the job.

Then the ratio of the time it takes B to complete the job to the time it takes A to complete the job is 

8 : 5, or 8x : 12.

Solving for x, 

we get 8x = 12, so x = 7 1/2 days.

 This is the number of days it takes B alone to complete the job.

A can complete the work in 6 days, so the amount of work he completes in 1 day is (1/6) of the total work.
B can complete the work in 8 days, so the amount of work he completes in 1 day is (1/8) of the total work.
With the help of C, they finish the work in 3 days, so the amount of work C contributes in 1 day is
(1/3) - [(1/6) + (1/8)] = 1/24 of the total work.
The ratio of the work done by A, B, and C in 1 day is
(1/6) : (1/8) : (1/24) = 4 : 3 : 1.
Therefore, A's share of the payment is Rs. (600 * 4/8) = Rs. 300.
B's share is Rs. (600 * 3/8) = Rs. 225.
C's share is Rs. [600 - (300 + 225)] = Rs. 75.