**Solution:** The correct answer is 32 days.

Explanation:

– Ajay’s efficiency is \( \frac{1}{32} \) of the work per day, as he can complete the work alone in 32 days.

– Let Bharat’s efficiency be \( x \). Therefore, Bharat completes \( x \) of the work per day.

Since Bharat starts the work and they work on alternate days, in 8 days Bharat will work for 4 days, and Ajay will also work for 4 days.

The total work done by Ajay in 4 days = \( 4 \times \frac{1}{32} = \frac{4}{32} = \frac{1}{8} \) of the total work.

The total work done by Bharat in 4 days = \( 4x \) (since Bharat works for 4 days).

According to the problem, the total work done by both Ajay and Bharat together in 8 days is equal to the entire work:

\( 4x + \frac{1}{8} = 1 \)

Solve for \( x \):

\( 4x = 1 – \frac{1}{8} = \frac{8}{8} – \frac{1}{8} = \frac{7}{8} \)

\( x = \frac{7}{32} \)

Bharat’s efficiency is \( \frac{7}{32} \) of the work per day. Therefore, the number of days Bharat alone would take to complete 1 unit of work is:

\( \frac{1}{\frac{7}{32}} = \frac{32}{7} \) days.

Since the question asks for the time Bharat would take to complete 7 times the work:

Time taken = \( 7 \times \frac{32}{7} = 32 \) days.

Therefore, Bharat alone can finish 7 times the same work in **32 days**.