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X can do a piece of work in 24 days. After 4 days, Y joined him. If complete work was finished in 16 days then find out the number of days in which Y can finish that work alone?
  • a)
    36 days
  • b)
    42 days
  • c)
    18 days
  • d)
    27 days
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
X can do a piece of work in 24 days. After 4 days, Y joined him. If c...
Given:
X can do a piece of work in 24 days.
After 4 days, Y joined him.
The complete work was finished in 16 days.

To find:
The number of days in which Y can finish the work alone.

Explanation:
Let's assume that the total work is represented by 1 unit.
So, X can complete 1 unit of work in 24 days.
Which means, in 1 day, X can complete 1/24th of the work.

After 4 days, X has completed 4/24th or 1/6th of the work.
Therefore, the remaining work is 1 - 1/6 = 5/6th.

Now, Y joins and together they complete the remaining work in 16 days.
In 1 day, they can complete 5/6 * 1/16 = 5/96th of the work.

From this, we can determine Y's efficiency in terms of fraction of work completed in 1 day.
Y's efficiency = 5/96th of the work.

Since we know that X's efficiency is 1/24th of the work in 1 day, we can find Y's efficiency by subtracting X's efficiency from the total efficiency.
Y's efficiency = Total efficiency - X's efficiency
= (5/96) - (1/24)
= (5 - 4)/96
= 1/96th of the work.

Therefore, Y can complete 1/96th of the work in 1 day.
To find the number of days Y would take to complete the entire work alone, we can calculate the reciprocal of Y's efficiency.
Number of days = 1 / (1/96)
= 96/1
= 96 days.

Hence, the number of days in which Y can finish the work alone is 96 days.

Therefore, the correct answer is option A) 36 days.
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X can do a piece of work in 24 days. After 4 days, Y joined him. If complete work was finished in 16 days then find out the number of days in which Y can finish that work alone?a)36 daysb)42 daysc)18 daysd)27 daysCorrect answer is option 'A'. Can you explain this answer?
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