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Sanjay can do a piece of work in 50 days. He started the work and left after some days, when 25% work was done. After it Ajit joined and completed it working for 25 days. In how many days Sanjay and Ajit can do the complete work, working together?
- a)6
- b)8
- c)10
- d)12
- e)20
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
Sanjay can do a piece of work in 50 days. He started the work and left...
Efficiency of Sanjay = (100/50) = 2%
Rest work = 75%
∴ Efficiency of Ajit = 75/25 = 3%
∴ Combined efficiency of Sanjay and Ajit = 5%
∴ Number of days required by Sonu and Abhijeet, to work together = 100/5 = 20 days.
Rest work = 75%
∴ Efficiency of Ajit = 75/25 = 3%
∴ Combined efficiency of Sanjay and Ajit = 5%
∴ Number of days required by Sonu and Abhijeet, to work together = 100/5 = 20 days.
Most Upvoted Answer
Sanjay can do a piece of work in 50 days. He started the work and left...
To solve this problem, we need to first find the individual rates at which Sanjay and Ajit work. Once we have those rates, we can determine how long it would take them to complete the work together.
Let's start by finding Sanjay's rate of work. We know that he can complete the entire work in 50 days. Therefore, his rate of work can be calculated as:
Sanjay's rate = 1 work / 50 days = 1/50
Now, let's determine how much work Sanjay completed before leaving. We are given that he left when 25% of the work was done. Therefore, the amount of work completed by Sanjay can be calculated as:
Sanjay's work = 25% of total work = 25/100 = 1/4
Since Sanjay left after completing 1/4 of the work, the remaining work that Ajit needs to complete can be calculated as:
Remaining work = 1 - Sanjay's work = 1 - 1/4 = 3/4
Now, let's find Ajit's rate of work. We are given that Ajit completed the remaining work in 25 days. Therefore, his rate of work can be calculated as:
Ajit's rate = Remaining work / Time taken = (3/4) / 25 = 3/100
Now that we have the individual rates of work for both Sanjay and Ajit, we can determine how long it would take them to complete the work together. Let's denote the time taken by both Sanjay and Ajit to complete the work together as T.
The combined work done by Sanjay and Ajit in time T can be calculated as:
Sanjay's work + Ajit's work = 1
Using the rates of work we calculated earlier, we can write the equation as:
(Sanjay's rate * T) + (Ajit's rate * T) = 1
Substituting the values of the rates, we get:
(1/50 * T) + (3/100 * T) = 1
Multiplying both sides of the equation by 100 to eliminate the fractions, we get:
2T + 3T = 100
5T = 100
T = 100/5
T = 20
Therefore, Sanjay and Ajit can complete the entire work together in 20 days. So, the correct answer is option E.
Let's start by finding Sanjay's rate of work. We know that he can complete the entire work in 50 days. Therefore, his rate of work can be calculated as:
Sanjay's rate = 1 work / 50 days = 1/50
Now, let's determine how much work Sanjay completed before leaving. We are given that he left when 25% of the work was done. Therefore, the amount of work completed by Sanjay can be calculated as:
Sanjay's work = 25% of total work = 25/100 = 1/4
Since Sanjay left after completing 1/4 of the work, the remaining work that Ajit needs to complete can be calculated as:
Remaining work = 1 - Sanjay's work = 1 - 1/4 = 3/4
Now, let's find Ajit's rate of work. We are given that Ajit completed the remaining work in 25 days. Therefore, his rate of work can be calculated as:
Ajit's rate = Remaining work / Time taken = (3/4) / 25 = 3/100
Now that we have the individual rates of work for both Sanjay and Ajit, we can determine how long it would take them to complete the work together. Let's denote the time taken by both Sanjay and Ajit to complete the work together as T.
The combined work done by Sanjay and Ajit in time T can be calculated as:
Sanjay's work + Ajit's work = 1
Using the rates of work we calculated earlier, we can write the equation as:
(Sanjay's rate * T) + (Ajit's rate * T) = 1
Substituting the values of the rates, we get:
(1/50 * T) + (3/100 * T) = 1
Multiplying both sides of the equation by 100 to eliminate the fractions, we get:
2T + 3T = 100
5T = 100
T = 100/5
T = 20
Therefore, Sanjay and Ajit can complete the entire work together in 20 days. So, the correct answer is option E.
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