Time and Work

A's work rate is 1/15 of the project per day,
and B's work rate is 1/20 of the project per day.
When they work together,
their combined work rate is 7/60 of the project per day.
Over a 4-day period,
they have completed 7/15 of the project.
The remaining work is therefore 8/15 of the project, which means that they still have 8/15 of the project left to complete

According to the calculation, the ratio of Kim's wages to David's wages is 2:3,
which means that for every 2 units of wages that Kim receives,
David receives 3 units of wages.
The calculation also shows that the ratio of Kim's work rate to David's work rate is 2:3,
with Kim able to complete 1/3 of the work in a day and David able to complete 1/2 of the work in a day.
Using this information,
we can determine that Kim's share of the total payment of Rs. 150 is Rs. 60,
which is equal to 2/5 of the total payment

According to the calculation,
the ratio of the time it takes Sakshi to complete the work to the time it takes Tanya to complete the work is 5:4.
This means that for every 5 units of time it takes Sakshi to complete the work,
it takes Tanya 4 units of time.
Using this information,
we can determine that Tanya will take 16 days to complete the work.
This is calculated by setting up a proportion using the ratio of the time it takes Sakshi to complete the work to the time it takes Tanya to complete the work and the known value of 20 days for Sakshi.
The proportion is 5:4 :: 20:x,
and solving for x gives us a value of 16 days

According to the calculation,
the ratio of the number of men to the number of women required to reap the field is 1:3/2.
This means that for every 1 man,
3/2 women are required.
The calculation also shows that the total number of men and women required to reap the field is equivalent to 28 women.
Using this information,
we can determine that it will take 28 women,
or the equivalent number of men and women,
9 days to reap the field.
This is because 18 women can reap the field in 14 days,
and 28 women is a greater number,
so it will take longer to complete the work

To solve this system of equations,
we can use algebraic methods.
Here's how you can solve for x in the given system of equations:
First, we start with the equation x * 9 = (x + 10) * 6.
We can simplify this equation by combining like terms on the right-hand side, which gives us
x * 9 = 6x + 60.
Now we can subtract 6x from both sides of the equation to get 3x = 60.
Dividing both sides of the equation by 3 gives us x = 20.
So, the solution to the system of equations is x = 20.

To solve this equation, we can use algebraic methods. Here's how you can solve for x:
First, we start with the equation 10/40 + 10/30 + 10/x = 1.
We can simplify each fraction by dividing the numerator and denominator by their greatest common factor, which gives us (1/4) + (1/3) + (10/x) = 1.
Now we can add (1/4) and (1/3) to get (7/12) + (10/x) = 1.
Subtracting (7/12) from both sides of the equation gives us (10/x) = (5/12).
Multiplying both sides of the equation by x gives us 10 = (5/12) * x.
Multiplying both sides of the equation by 12/5 gives us x = 24.
So, the solution to the equation is x = 24.
This means that it would take C alone 24 days to do the entire job

If it takes Varma k minutes to read an entire book,
then the fraction of the book that he can read in 1 minute is 1/k.
Similarly,
if it takes him 8 minutes to read a book,
the fraction of the book that he can read in 8 minutes is 8/k

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

(A+B)'s 1 day work = 1/12,
(B+C)'s 1 day work = 1/15,
(C+A)'S 1 day work = 1/20
Including: 2(A+B+C)'s 1 day work = (1/12+ 1/15+ 1/20)= 12/60 = 1/5
∴ (A+B+C) `s 1 day work = (1/2 *1/5) = 1/10
∴ working together they can complete the work in 10 days.
A's 1 day work = (1/10-1/15) = 1/30, B`s 1 day work = (1/10-1/20) = 1/20
C's 1 day work = (1/10-1/12) = 1/60
∴ A alone can take the necessary steps in 30 days

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.

The total amount of work that A, B, and C can complete in 1 day is (A+B+C) 1 days work = 1/10.
This means that in 10 days, they will be able to complete 10 * (A+B+C) 1 days work = 10 * (1/10) = 1 unit of work.
Since we know that the task requires 1 unit of work to be completed, this means that A, B, and C will be able to complete the task in 10 days.

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.

Based on the information given, it can be calculated that C's individual contribution to completing the job in one day is equal to the total work done by A, B, and C in one day minus the total work done by A and B in one day.
If we let "x" represent the amount of work that C can do in one day, then the equation would be:v x = (A+B+C)'s one day work - (A+B)'s one day work
Using the information provided, we can substitute the values and solve for x:
x = (Apti Time and work 52) - (Apti Time and work 51)
x = Apti Time and work 53
Therefore, C can complete the job in 15 days if they work individually at a rate of Apti Time and work 53 per day.

It takes 33 days for 6 women or 17 men to paint a wall.
The work rate of 12 women and 32 men can be calculated by converting the work rate of 6 women to men,
which is 17/6 men/woman.
The total work rate of the group of 12 women and 32 men is then 34 men.
Therefore, it would take (17*33)/34 = 25.5 days for 12 women and 32 men to paint three walls at the same rate

The work rate of A is 1/20 of the task per day,
while the work rate of B and C together is 1/10 of the task per day.
When A is assisted by B and C every third day,
they can complete 1/5 of the task in 3 days.
Therefore, it will take A a total of 15 days to complete the task on their own.

The work rate of C is 1/24 of the task per day,
while the work rate of A is 1/6 of the task per day and the work rate of B is 1/8 of the task per day.
The ratio of their wages is 4:3:1,
with C receiving a 1/8 share.
Therefore, C's share of the total cost of Rs. 3200 for completing the task in 3 days is Rs. 400.

If the work rate of one man is represented by 'x' and the work rate of one boy is represented by 'y',
the work rates of 6 men and 8 boys can be represented as
6x + 8y = 1/10.
Similarly, the work rates of 26 men and 48 boys can be represented as
26x + 48y = 1/2.
Solving these equations,
we find that the work rate of one man is 1/100 of the task per day and the work rate of one boy is 1/200 of the task per day.
Therefore, 15 men and 20 boys can complete the task in 4 days

If the work rate of A is 1/4 of the task per hour, the work rate of B and C together is 1/3 of the task per hour,
and the work rate of A and C together is 1/2 of the task per hour,
then the work rate of B alone is (1/3 - 1/4) of the task per hour.
Therefore, B will take 12 hours to complete the task on their own.

If the work rate of A and B together is 1/10 of the task per day,
the work rate of C is 1/50 of the task per day,
and the combined work rate of A, B, and C is 1/6 of the task per day,
then the work rate of A is equal to the combined work rate of B and C.
Therefore, the work rate of B is (1/6 - 1/50) of the task per day,
or 1/25 of the task per day.
This means that B can complete the task in 25 days on their own

If the work rate of one man is represented by 'x' and the work rate of one woman is represented by 'y',
the work rates of 4 men and 6 women can be represented as
4x + 6y = 1/8.
Similarly,
the work rates of 3 men and 7 women can be represented as
3x + 7y = 1/10.
Solving these equations,
we find that the work rate of one woman is 1/400 of the task per day.
Therefore, 10 women can complete the task in 40 days

The work rate of A and B together is 1/30 of the task per day,
and they work together for 20 days, completing 2/3 of the task.
The remaining work is 1/3 of the task, which A finishes in 20 days.
This means that A's work rate is 1/3 of the task per day.
Therefore, it will take A 60 days to complete the task on their own.

The work rate of one woman is 1/70 of the task per day,
and the work rate of one child is 1/140 of the task per day.
The combined work rate of 5 women and 10 children is (5/70 + 10/140) of the task per day,
which is equal to 1/14 of the task per day.
Therefore, it will take 5 women and 10 children a total of 7 days to complete the task

The work rate of X is 1/20 of the task per day, and the work rate of Y is 1/12 of the task per day. X works alone for 4 days, completing 1/5 of the task.
The remaining work is 4/5 of the task, and the combined work rate of X and Y is 2/15 of the task per day.
Therefore, it will take X and Y a total of 6 days to complete the remaining work.
The total time taken for the work to be completed is 6 days + 4 days = 10 days

If the ratio of the time it takes Sakshi and Tanya to complete the same task is 5:4,
and it takes Sakshi 20 days to complete the task,
then it will take Tanya 16 days to complete the task.
This is because Tanya is 25% more efficient than Sakshi,
and the ratio of their work rates can be expressed as 5:4,
with Tanya's work rate being 4/5 of Sakshi's work rate.

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

The combined work rate of A and B is 1/6 of the task per day, and they work together for 2 days,
completing 1/3 of the task.
The remaining work is 2/3 of the task, and A's work rate is 1/15 of the task per day.
Therefore, it will take A 10 days to complete the remaining work.
The total time taken for the task to be completed is 10 days + 2 days = 12 days

If the combined work rate of A, B, and C is 1/8 of the task per day,
and they work together for 10 days, completing 5/8 of the task,
the remaining work is 3/8 of the task.
The work rate of A is 1/24 of the task per day, so it will take A 18 days to complete the remaining work.
Therefore, A will take a total of 18 days to finish the work after B and C leave.

"If B's work rate is 1/12 of the task per day,
and A's work rate is twice as fast as B's, meaning it is 1/6 of the task per day,
then the combined work rate of A and B is
(1/6 + 1/12) of the task per day, which is equal to 1/4 of the task per day.
Therefore, it will take A and B 4 days to complete the work together.

If the combined work rate of A, B, and C is 1/6 of the task per day,
the work rate of A and B is 1/8 of the task per day,
and the work rate of B and C is 1/12 of the task per day,
then the work rate of A and C is
(2 x 1/8 - 1/12) of the task per day,
which is equal to 1/8 of the task per day.
Therefore, A and C will take 8 days to complete the work together

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

If we let A's 1 day's work be represented by x and B's 1 day's work be represented by y,
then the equations x + y = 1 and 16x + 44y = 1 can be used to determine that x = 1 and y = 1.
This means that B's 1 day's work is equal to 1.
Therefore, B alone will take 60 days to finish the entire work

A and B together can complete the work in 4 days,
so the amount of work they complete in 1 day is (1/4) of the total work.
A alone can complete the work in 12 days, so the amount of work he completes in 1 day is (1/12) of the total work.
The amount of work B completes in 1 day is the total amount of work completed by A and B in 1 day minus the amount of work A completes in 1 day.
This is (1/4) - (1/12) = (1/6) of the total work.
Since B completes (1/6) of the total work in 1 day, it will take him 6 days to complete the entire work.

A can complete the work in 7 days, working 9 hours per day,
so he takes a total of 7 * 9 = 63 hours to complete the work.
Similarly, B takes a total of 6 * 7 = 42 hours to complete the work.
A's 1 hour's work is (1/63) of the total work, and B's 1 hour's work is (1/42) of the total work.
When they work together, their combined 1 hour's work is (1/63) + (1/42) = (5/126) of the total work.
Since they are working 8 hours per day, it will take them 126 / (5 * 8) = 3 days to complete the 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 80 days,

so the amount of work he completes in 1 day is (1/80) of the total work.

A works on the job for 10 days, 

so he completes a total of (1/80) * 10 = 1/8 of the total work.

The remaining work is 1 - 1/8 = 7/8 of the total work.

B alone finishes the remaining work in 42 days, so the amount of work he completes in 1 day is 

(7/8) / 42 = 1/48 of the total work.

When A and B work together, their combined 1 day's work is 

(1/80) + (1/48) = 8/240 = 1/30 of the total work.

Since they complete (1/30) of the total work in 1 day, 

it will take them 30 days to complete the entire work.

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.

Let's suppose that the work done by 1 man in 1 day is x, and the work done by 1 boy in 1 day is y.

Then the work done by 2 men and 3 boys in 1 day is 2x + 3y, and the work done by 3 men and 2 boys in 1 day is 3x + 2y.

We are given that 2 men and 3 boys can complete the work in 10 days, so 2x + 3y = 1/10.

We are also given that 3 men and 2 boys can complete the work in 8 days, so 3x + 2y = 1/8.

Solving these equations for x and y, we get x = 7/200 and y = 1/100.

The work done by 2 men and 1 boy in 1 day is (2 * 7/200) + (1/100) = 16/200 = 2/25 of the total work.

Since 2 men and 1 boy complete (2/25) of the work in 1 day, it will take them 25/2 = 12 1/2 days to complete the entire work.