Question : To do certain work, Ajay and Bharat work on alternate days, with Bharat starting the work on the first day. Ajay can finish the work alone in 32 days. If the work gets completed in exactly 8 days, then Bharat alone can finish 7 times the same work in _______ days.
Option 1: $\frac{28}{8}$
Option 2: $4$
Option 3: $\frac{32}{7}$
Option 4: $32$
Correct Answer: $32$
Solution :
Given: Ajay can finish the work alone in 32 days.
Efficiency of Ajay = $\frac{1}{32}$
Ajay and Bharat completed the work in exactly 8 days.
So, both will work for 4 days each alternatively.
Total work of Ajay = $4×\frac{1}{32}=\frac{1}{8}$
Total work of Bharat = $1–\frac{1}{8}=\frac{7}{8}$
Bharat completed $\frac{7}{8}$ work in 4 days.
So, 1 day work of Bharat = $\frac{7}{8×4}=\frac{7}{32}$
Therefore Bharat will take $\frac{32}{7}$ days to finish the work alone.
Bharat alone can finish 7 times the same work in = $7×\frac{32}{7}=32$ days
Hence, the correct answer is $32$.
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