 Math »
 P and S can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which S was replaced by A. If the work would be finished in next 5 days,..
P and S can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which S was replaced by A. If the work would be finished in next 5 days,..
Learn how two workers, P and S, contribute to completing a task within specified time frames. After collaborating for a period, S is substituted with A, leading to the task's completion in a given time. Unravel the time it takes for A to finish the job individually.
by Maivizhi A
Updated Mar 18, 2024
P and S can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which S was replaced by A. If the work would be finished in next 5 days, Find the number of days in which A alone could complete the work.
A alone can complete the work in 40 days.
Let's find the number of days A alone can complete the work.
1. Calculate the combined work rate of P and S:
 P's work rate per day = 1/20 (as P can complete the work in 20 days)
 S's work rate per day = 1/15 (as S can complete the work in 15 days)
 Combined work rate of P and S = P's rate + S's rate = 1/20 + 1/15 = 7/60 (work completed per day by both P and S)
2. Find the work completed by P and S in 6 days:
 Work done by P and S in 6 days = Combined rate * Time = 7/60 * 6 = 7/10 (work completed)
3. Calculate the remaining work:
 Total work = 1 (as the whole work needs to be done)
 Remaining work = Total work  Work done by P and S = 1  7/10 = 3/10
4. Find the combined work rate of P and A:
 We know the remaining work (3/10) is completed by P and A in 4 days.
 Let A's work rate per day be x.
 Combined rate of P and A = (Remaining work) / (Time taken) = 3/10 / 4 = 3/40
5. Express the combined rate in terms of P's and A's rates:
 Combined rate of P and A = P's rate + A's rate = 1/20 + x
6. Equate both expressions for the combined rate:
 1/20 + x = 3/40
 Solve for x (A's rate):
 x = 3/40  1/20
 x = 1/40
7. Find the number of days A alone can complete the work:
 A's rate per day = 1/40
 Time taken by A to complete the work = 1 / (A's rate) = 1 / (1/40) = 40 days
Therefore, A alone can complete the work in 40 days.
Time and Work in Mathematics
Time and work problems are a common type of mathematical problem that involve determining the amount of time it takes for a certain number of workers, working at a certain rate, to complete a task. These problems often involve concepts of rates, proportions, and basic arithmetic.
Here's a general approach to solving time and work problems:

Understand the problem: Read the problem carefully and identify what needs to be solved. Understand the given information, such as the number of workers, their individual rates of work, and the task to be completed.

Identify the variables: Typically, you'll have variables such as the number of workers, the rate at which they work, and the time taken to complete the task. Assign variables to these quantities.

Formulate the equation: Use the concept that work done equals the product of the rate of work and the time taken. The basic equation is:
Total work = (Rate of work of one worker) × (Number of workers) × (Time taken)
Alternatively, you can also use the formula:
Total work = (1/Time taken) × (Number of workers)

Solve the equation: Once you have the equation, solve it to find the unknown quantity, which could be the time taken, the rate of work, or the number of workers.

Check your answer: Ensure that your solution makes sense in the context of the problem. Sometimes, it's helpful to doublecheck your calculations to avoid errors.
Let's consider an example:
Example: If it takes 6 hours for 8 workers to complete a task, how long will it take for 12 workers to complete the same task?
Solution:

Understand the problem: We want to find out how long it takes for 12 workers to complete a task if it took 8 workers 6 hours.

Identify the variables: Let T be the time taken for 12 workers to complete the task.

Formulate the equation:
 For 8 workers: 6 = (1/T) × 8
 For 12 workers: Total work = (1/T) × 12

Solve the equation:
 From the equation for 8 workers: T = 8/6 = 4/3 hours.
 Substitute T = 4/3 into the equation for 12 workers: Total work = 1 / (4/3) × 12 = 9 hours.

Check your answer: It makes sense that it takes less time with more workers, so 9 hours seems reasonable.
P and S can complete a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which S was replaced by A  FAQs
1. What are the individual work rates of P and S?
P's work rate per day is 1/20, and S's work rate per day is 1/15.
2. How long do P and S take to complete the work together?
Together, P and S can complete the work in 7/60 of the work per day.
3. How much work can P and S complete together in 6 days?
P and S together can complete 7/10 of the work in 6 days.
Recent Updates
 Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevati...
 Aman’s salary is first increased by 25% and then decreased by 20%. The result is the ...
 A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find ...
 The numbers 33, 45 and 78, used in relation to vinyl records, refer to how much they co...
 Simplify (ab^2 c^3) * (a^4 b^5 c^6) / (a^7 b^8 c^9) * (a^10 b^11 c^12) * (a^13 b^1...
 A machine can print 12 page in a minute. How long will the machine take to print 5760 p...
 There are 20 points in a plane, how many triangles can be formed by these points if 5 a...
 The total cost of chocolates purchased by Sabu is ₹68.25. If the cost of one chocolat...
 One kg of basmati rice costs $ 43.75. find the cost of 17 1/2 kg of rice?
 A trader sold a cycle at a loss of 10%. If the selling price had been increased by Rs. ...
 In a garden, 2626 trees are planted at equal distances along a yard 300300 metres long,...
 A man plants 15376 apple trees in his garden and arranges them so that there are as man...
 The simple interest on a certain sum for 3 years in Rs. 225 and the compound interest o...
 p is thrice as good a workman as q and therefore able to finish a job in 48 days less t...
 If a and b together can complete a piece of work in 15 days and b alone in 20 days, in ...