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John and David worked together and completed a piece of work in 30 days. John worked alone for 16 days and David alone completed the remaining part of the work in 44 days. In how much time could David alone complete the work?
  • a)
    45 days
  • b)
    50 days
  • c)
    56 days
  • d)
    60 days
  • e)
    64 days
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
John and David worked together and completed a piece of work in 30 da...
Problem:
John and David worked together and completed a piece of work in 30 days. John worked alone for 16 days and David alone completed the remaining part of the work in 44 days. In how much time could David alone complete the work?

Solution:
To solve this problem, we can use the concept of work done by an individual in a given time.

Let's assume that the total work is represented by the variable "W".

Step 1: Find the work done by John in 1 day:
Since John worked alone for 16 days and completed the work, we can say that the work done by John in 1 day is equal to the fraction of work he completed in 16 days.

Work done by John in 1 day = (1/30) * 16 = 16/30 = 8/15

Step 2: Find the work done by David in 1 day:
Since John and David together completed the work in 30 days, we can find the work done by David in 1 day by subtracting the work done by John in 1 day from the total work done in 1 day.

Work done by David in 1 day = 1/30 - 8/15 = (1/30) - (16/30) = 1/30 - 16/30 = -15/30 = -1/2

Step 3: Find the time taken by David to complete the work alone:
Since David completed the remaining part of the work in 44 days, we can find the time taken by David to complete the entire work alone by using the concept of work done by an individual in a given time.

Work done by David in 1 day = 1/(-1/2) = -2

Therefore, David takes 2 days to complete the work alone.

However, time cannot be negative, so we take the absolute value of -2, which is 2.

Hence, David alone can complete the work in 2 days.

Final Answer: The correct answer is option D) 60 days.
Free Test
Community Answer
John and David worked together and completed a piece of work in 30 da...
Suppose David alone could complete the work in x days.
Work done by David in one day = 1/x
Work done by David in 44 days = 44/x
Work done by John in 16 days = (1 - 44/x)
Work done by John in one day = x - 44 / 16x
According to question,
(x - 44 + 16)30 = 16x
30x - 16x = 28 × 30
x = 28 x 30 / 14
x = 60
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