A) 10 days
B) 8 days
C) 12 days
D) 15 days
Correct Answer: A
Solution :
One day's work of \[A=\frac{1}{15}\] One day's work of \[B=\frac{1}{10}\] Two day's work of A and B together \[=2\left( \frac{1}{15}+\frac{1}{10} \right)=\frac{1}{3}\] Remaining work \[=1-\frac{1}{3}=\frac{2}{3}\] \[\overset{Work}{\mathop{_{\frac{2}{3}}^{1}\mathop{\downarrow }_{{}}^{{}}}}\,\] \[\overset{Days}{\mathop{_{x}^{15}\mathop{\downarrow }_{{}}^{{}}}}\,\] \[\therefore \] \[1:\frac{2}{3}::15:3\] \[\Rightarrow \] \[x=\frac{2\times 15}{13}=10\] \[\therefore \] The whole work is completed in 12 days.
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