Select the correct answerX and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?Options6 days15 days20 days10 days
Question
Select the correct answerX and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?Options6 days15 days20 days10 days
Solution
To solve this problem, we need to first find out the work done by X and Y in one day.
- X can complete the work in 20 days. So, the work done by X in one day is 1/20.
- Y can complete the work in 12 days. So, the work done by Y in one day is 1/12.
Now, let's calculate the work done by X in the first 4 days. Since X can do 1/20 of the work in one day, in 4 days he will do 4*(1/20) = 1/5 of the work.
The remaining work is 1 - 1/5 = 4/5.
Now, X and Y work together to complete the remaining work. In one day, X and Y together can do (1/20 + 1/12) = 8/120 = 1/15 of the work.
So, to complete the remaining 4/5 of the work, X and Y will take (4/5) / (1/15) = 12 days.
Therefore, the total time taken to complete the work is 4 days (X alone) + 12 days (X and Y together) = 16 days.
So, none of the options given are correct. The work lasted for 16 days.
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