A can do a certain work in 12 days. B is 60% more efficient then A. How many days will B and A together take to do the same job?

Answer: Option D

Time taken by B to complete the work
$$\begin{array}{rl}& =12\times \frac{100}{160}\\ & =\frac{15}{2}\text{days}\end{array}$$
∴ (A + B)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{12}+\frac{2}{15}\\ & =\frac{5+8}{60}\\ & =\frac{13}{60}\end{array}$$
Hence, the work will be completed in $$\frac{60}{13}$$ days

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Alternate:
Ratio of time, taken by A and B = 160 : 100 = 8 : 5
If A takes 8 days, B takes 5 days.
If A takes 12 days, B takes = $$\frac{5}{8}\times 12=\frac{15}{2}$$
Time take by A = 12 days
Time take by B = 7.5 days
L.C.M. of Total Work = 60
Ratio of time, taken by A and B = 8 : 5
Time taken by A and B together to complete the task
$$=\frac{60}{13}\text{days}$$