X can do a piece of work in 20 days and Y can do it in 12 days. Y worked at it for 9 days. In how many days can X alone finish the remaining work?

Steps to Solve

1. Find the work rate of X and Y
   X can complete the work in 20 days, so X's work rate is:
   $$ \text{Work Rate of X} = \frac{1}{20} $$
   Y can complete the work in 12 days, so Y's work rate is:
   $$ \text{Work Rate of Y} = \frac{1}{12} $$

2. Calculate the work done by Y in 9 days
   In 9 days, Y does the following amount of work:
   $$ \text{Work done by Y} = 9 \times \text{Work Rate of Y} = 9 \times \frac{1}{12} = \frac{9}{12} = \frac{3}{4} $$
   This means Y completed 75% of the work.

3. Determine the remaining work
   The remaining work that needs to be completed is:
   $$ \text{Remaining Work} = 1 - \text{Work done by Y} = 1 - \frac{3}{4} = \frac{1}{4} $$

4. Calculate the time taken by X to finish the remaining work
   To find out how long it will take X to complete the remaining ( \frac{1}{4} ) of the work:
   $$ \text{Time taken by X} = \frac{\text{Remaining Work}}{\text{Work Rate of X}} = \frac{\frac{1}{4}}{\frac{1}{20}} = \frac{1}{4} \times \frac{20}{1} = 5 $$