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Prakash is twice as fast as sumit and therefore Prakash is able to finish the work in 30 days less than sumit. Find the time in which they can complete the work when both are working together?
- a)25 days
- b)20 days
- c)30 days
- d)35 days
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Prakash is twice as fast as sumit and therefore Prakash is able to fin...
Let sumit take x days then Prakash will take x/2 days to complete the work.
X – X/2 = 30, X = 60
1/60 + 1/30 = 1/d so, we will get d= 20 days
X – X/2 = 30, X = 60
1/60 + 1/30 = 1/d so, we will get d= 20 days
Most Upvoted Answer
Prakash is twice as fast as sumit and therefore Prakash is able to fin...
To solve this problem, let's assume that Sumit takes x days to complete the work.
According to the given information, Prakash is twice as fast as Sumit. Therefore, Prakash will take x/2 days to complete the work.
It is also given that Prakash is able to finish the work in 30 days less than Sumit. This means that Prakash takes 30 days less than Sumit to complete the work.
So, we can write the equation:
x - (x/2) = 30
Simplifying the equation, we have:
2x - x = 60
x = 60
Therefore, Sumit takes 60 days to complete the work.
Now, let's find the time in which they can complete the work when both are working together.
Let's assume that when both Prakash and Sumit work together, they can complete the work in t days.
The work done by Prakash in one day = 1/(x/2) = 2/x
The work done by Sumit in one day = 1/x
When they work together, their combined work in one day = 2/x + 1/x = 3/x
Since we know that they can complete the work in t days, we can write the equation:
(3/x) * t = 1
Simplifying the equation, we have:
t = x/3
Substituting the value of x, we get:
t = 60/3
t = 20
Therefore, when Prakash and Sumit work together, they can complete the work in 20 days.
Hence, the correct answer is option B) 20 days.
According to the given information, Prakash is twice as fast as Sumit. Therefore, Prakash will take x/2 days to complete the work.
It is also given that Prakash is able to finish the work in 30 days less than Sumit. This means that Prakash takes 30 days less than Sumit to complete the work.
So, we can write the equation:
x - (x/2) = 30
Simplifying the equation, we have:
2x - x = 60
x = 60
Therefore, Sumit takes 60 days to complete the work.
Now, let's find the time in which they can complete the work when both are working together.
Let's assume that when both Prakash and Sumit work together, they can complete the work in t days.
The work done by Prakash in one day = 1/(x/2) = 2/x
The work done by Sumit in one day = 1/x
When they work together, their combined work in one day = 2/x + 1/x = 3/x
Since we know that they can complete the work in t days, we can write the equation:
(3/x) * t = 1
Simplifying the equation, we have:
t = x/3
Substituting the value of x, we get:
t = 60/3
t = 20
Therefore, when Prakash and Sumit work together, they can complete the work in 20 days.
Hence, the correct answer is option B) 20 days.
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