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?

Solution(By Examveda Team)

Time taken by B to complete the work
$$\eqalign{ & = 12 \times \frac{{100}}{{160}} \cr & = \frac{{15}}{2}\,{\text{days}} \cr} $$
∴ (A + B)'s 1 day's work
$$\eqalign{ & = \frac{1}{{12}} + \frac{2}{{15}} \cr & = \frac{{5 + 8}}{{60}} \cr & = \frac{{13}}{{60}} \cr} $$
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
$$ = \frac{{60}}{{13}}{\text{days}}$$