X and Y together can finish a task in 20 days. Y alone can finish the same task in 25 days. In how many days can X alone finish the task?

Correct option is C

Given:

X and Y can finish task in 20days

Y can finish task in 25days

Formula Used:

Let total work be 1.

Then work done 1 day = $$\frac{1}{Total\ time\ to\ work}$$​ 

Solution:

X and Y’s one day’s work = $$\frac{1}{20}$$​​

Y’s one day’s work =$$\frac{1}{25}$$​​

X’s one day work =$$\frac{1}{20} - \frac{1}{25} = \frac{5-4}{100} = \frac{1}{100}$$​​

Time taken by X to finish the work = $$\frac{Total\ Work}{X’s\ one\ day’s\ work} = \frac{1}{\frac{1}{100}}$$ = 100 days

Alternative Method:

Total Work = Efficiency $$\times$$​ Time

Total Work = LCM of 20 and 25 = 100

Efficiency of X and Y together = $$\frac{100}{20}$$ = 5 units per day.

Efficiency of Y = $$\frac{100}{25}$$ = 4 units per day

Efficiency of X = 5 - 4 =1units per day

Time taken by X to complete the work = $$\frac{100}{1}$$ =100 days