A is thrice as efficient as B. A started working and after 4 days he was replaced by B. B then worked for 15 days and left. If A and B toge…

Solution
Rate of doing work by A and B is $\frac{1}{A} $ and $\frac{1}{B}$
$\frac{1}{A} $ = $\frac{3}{B}$
In 4 days A would have completed $\frac{4}{A}$ or $\frac{12}{B}$ amount of work
In 15 days B would have completed $\frac{15}{B}$ amount of work
Since total work done was 75%.
$\frac{12}{B} + \frac{15}{B} = \frac{3}{4}$
$\frac{27}{B} = \frac{3}{4}$
$\frac{1}{B} = \frac{1}{36}$
B alone would take 36 days to complete the work.
Option D is the correct answer.

Solution
Rate of doing work by A and B is $\frac{1}{A} $ and $\frac{1}{B}$
$\frac{1}{A} $ = $\frac{3}{B}$
In 4 days A would have completed $\frac{4}{A}$ or $\frac{12}{B}$ amount of work
In 15 days B would have completed $\frac{15}{B}$ amount of work
Since total work done was 75%.
$\frac{12}{B} + \frac{15}{B} = \frac{3}{4}$
$\frac{27}{B} = \frac{3}{4}$
$\frac{1}{B} = \frac{1}{36}$
B alone would take 36 days to complete the work.
Option D is the correct answer.