A) 18 days
B) 26 days
C) 20 days
D) 21 days
E) None of these
Correct Answer: C
Solution :
Work done by A in 1 day\[=\frac{1}{12}\] Work done by B in 1 day\[=\frac{1}{36}\] Both can finish the work in 1 day \[=\frac{1}{12}+\frac{1}{36}=\frac{3+1}{36}=\frac{4}{36}=\frac{1}{9}\] in 4 days both finish the work\[=4\times \frac{1}{9}=\frac{4}{9}\] Now, remaining work\[=1-\frac{4}{9}=\frac{5}{9}\] Hence the remaining work is done by B in\[36\times \frac{5}{9}=20\]days Quicker Method: Let total work\[=36\]units (L.CM of 12 and 36) Now, A can finish \[\frac{36}{12}=3\]units/day B can finish \[\frac{36}{36}=1\] unit/day Now, in 4 days (A+ B) can finish \[(3+1)\times 4\]\[=4\times 4=16\] units \[\therefore \] Remaining work\[=36-16=20\]units 20 units work is done by B in\[=\frac{20}{1}=20\]days
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