Ajeet works 4 times as fast as Sohan. If Sohan can complete a work in 20 days independently, the number of days in which Ajeet and Sohan can together finish the work is:

Ajeet works 4 times as fast as Sohan.

Sohan can complete the work in 20 days.

Work done per day = $$\frac{1}{\text{number of days to complete the work}}.$$​​

Combined work = Work by Ajeet per day+Work by Sohan per day

Time taken by both together = $$\frac{1}{\text{Combined work per day}}$$​​

Sohan can complete the work in 20 days,

so Sohan's work per day = $$\frac{1}{20}$$​ of the total work.

Ajeet works 4 times as fast as Sohan,

so Ajeet’s work per day =$$4 \times \frac{1}{20} = \frac{4}{20} = \frac{1}{5}$$​ of the total work.

Combined work per day = $$\frac{1}{5} + \frac{1}{20}​.$$​​

​$$\frac{1}{5} + \frac{1}{20} = \frac{4}{20} + \frac{1}{20} = \frac{5}{20} = \frac{1}{4}.$$​​

If Ajeet and Sohan together complete $$\frac{1}{4}$$​ of the work in 1 day,

then the total time taken to complete the work is:

​$$\text{Time} = \frac{1}{\frac{1}{4}} = 4 \text{ days}.$$​​

Therefore, Ajeet and Sohan can together finish the work in 4 days.

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