$A$ and $B$ can polish the floors of a building in 10 days.
Question:

$A$ and $B$ can polish the floors of a building in 10 days. A alone can do $\frac{1}{4}$ th of it in 12 days. In how many days can $B$ alone polish the floor?

Solution:

It is given that $\mathrm{A}$ and $\mathrm{B}$ can polish the floors of the building in 10 days.

$\therefore$ Work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\frac{1}{10}$

Now, A alone can do $\frac{1}{4}$ th of the work in 12 days.

$\therefore$ Time taken by $\mathrm{A}$ alone to do the complete work $=(4 \times 12)=48$ days

$\Rightarrow$ Work done by A in 1 day $=\frac{1}{48}$

Now, work done by $\mathrm{B}$ in 1 day $=$ Work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $-$ Work done by $\mathrm{A}$ in 1 day

$=\frac{1}{10}-\frac{1}{48}$

$=\frac{24-5}{240}=\frac{19}{240}$

Thus, B alone can polish the floor in $\frac{240}{19}$ days or $12 \frac{12}{19}$ days.

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