Calculation:Lets Assume total work = 1 unit\(\text{{A}'s }\!\!~\!\!\text{ Work }\!\!~\!\!\text{ rate }\!\!~\!\!\text{ }=\frac{1}{37}\text{unit }\!\!~\!\!\text{ per }\!\!~\!\!\text{ min}\) \({\rm{B's\;Work\;rate}} = \frac{1}{{45}}{\rm{unit\;per\;min}}\) In question it is given that B is turned off after some minutes then we can say that A work for complete 30 minutes.So in 30 minutes A will do, \(\frac{{30}}{{37}}{\rm{unit}}\) \({\rm{Remaining\;work\;}} = 1\;{\rm{unit}} - \frac{{30}}{{37}}{\rm{unit}} = \frac{7}{{30}}{\rm{\;unit}}\) \({\rm{Remaining\;work\;done\;by\;B\;is\;in}} = \frac{{45 \times 7}}{{37}}{\rm{min}} = 8.513 \cong 9{\rm{\;minutes}}\) Hence 9 min is the correct answer.