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# Time & Work

1.

Rindia can do a job in 10 days. Rakesh can do the same job in 5 days. In how many days they can complite the job if they work together?

Rindia can do a job in 10 days.
So efficiency of Rindia = 100/10 = 10%
Similarly, Rakesh's efficiency = 100/5 = 20%
Combined efficiency of Rindia + Rakesh per day becomes = 20 + 10 = 30 %
Now, we have to find out the number of days taken by both Rindia and Rakesh to do 100% work,
Since they can do 30% work in 1 day,
So, they will 100% work in 100/30 = 3.33 days

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2.

A can do a work in 30 days and B can complete the same work in 45 days. In how many days the work will be completed if both work together?

A completes the work in 30 days. A's one day work will be 1/30 of the work. B's one day work will be 1/45 of the work.
Both work together, in one day, 1/30 + 1/45 of the work will get over.
In one day 75/1350 of the work will get over. Which means the work will get over in 1350/75 days. The work will get completed in 18 days.

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3.

Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?

 A's one day work = 1 12
 B's one day work = 1 18
 (A + B)'s one day work = 1 + 1 = (18 + 12) = 30 = 1 12 18 (12 x 18) 216 7.2

Together, A & B will finish the work in 7.2 days.

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4.

A can do a work in 24 days and B can complete the same work in 12 days. In how many days the work will be completed if both work together?

A completes the work in 24 days. A's one day work will be 1/24 of the work.
B's one day work will be 1/12 of the work.
Both work together, in one day, 1/24 + 1/12 of the work will get over.
In one day 36/288 of the work will get over. Which means the work will get over in 288/36 days.
The work will get completed in 8 days.

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5.

A can do a piece of work in 10 days, and B can do the same work in 20 days. With the help of C, they finished the work in 4 days. C can do the work in how many days, working alone?

Their combined 4 day work = 4(1/10 + 1/15) = 12/20 = 3/5.
Remaining work = 1 – 3/5 = ⅖.
This means C did 2/5 work in 4 days, hence he can finish the complete work in 5/2 × 4 = 10 days.

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6.

Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?

Given that A and B can complete the work in 6 days A + B will do 1/6 of the work in 1 day => A + B = 1/6 ---> (1)
B and C can do the same job in 10 days, B + C will do 1/10 of the work in 1 day => B + C = 1/10 ---> (2)
C and A will do the same job in 7.5 days i.e., 15/2 days C + A will do 2/15 of the work in 1 day => C+ A = 2/15 ---> (3)
Adding all the above three equation we get 2 ( A + B + C ) = 1/6 + 1/10 + 2 /15 = 5/30 + 3/ 30 + 4 / 30 = 12 / 30 => A + B + C = 6 / 30 = 1 / 5
In one day A, B and C can finish 1/5 of the work => working together they will finish the work in 5 days.

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7.

A can do a work in 45 days and B can complete the same work in 36 days. In how many days the work will be completed if both work together?

A completes the work in 45 days. A's one day work will be 1/45 of the work.
B's one day work will be 1/36 of the work.
Both work together, in one day, 1/45 + 1/36 of the work will get over.
In one day 81/1620 of the work will get over.
Which means the work will get over in 1620/81 days. The work will get completed in 20 days.

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8.

In the beginning, Ram works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Ram is to finish this work at a stretch, how many hours will he take to finish this work?

Ram’s 16 hr work = 16/24 = 2/3. Remaining work = 1 – 2/3 = 1/3.
Using work and time formula: This will be completed in 1/3 × 18 i.e. 6 hrs.
So, total time taken to complete work = 16 + 6= 22 hrs.

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9.

Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.

Assume that Pooja completes the job in 'x' days.
So, Aarti will take '2x' days to complete the same job.

As Pooja takes 90 days less than Aarti, we get
x = 2x – 90
By solving this equation, we get x = 90 .
Thus, 2x = 2 x 90 = 180

Part of job done by Pooja in 1 day = 1/ 90
Part of job done by Aarti in 1 day = 1/180

(Part of job done together in 1 day) = (Part of job done by Pooja in 1 day) + (Part of job done by Aarti in 1 day)
= (1/90) + (1/180)
= 3/180
=1/60
(1/60)th part of whole job will be completed by Pooja and Aarti together in one day.

Therefore, the whole job will be completed in 60 days together.

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10.

A completes 60% of a task in 15 days and then takes the help of B and C. B is 50% as efficient as A is and C is 50% as efficient as B is. In how many more days will they complete the work?

A completes 60% of the task in 15 days i.e., he completes 4% of the task in a day.
B is 50% as efficient as A is, therefore, B will complete 2% of the task in a day.
C is 50% as efficient as B is, therefore, C will complete 1% of the task in a day.
Together, A, B and C will complete 4 + 2 + 1 = 7% of the work in a day.
They have another 40% of the task to be completed. Therefore, they will take 40 / 7 more days to complete the task.

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