A does 20% less work than B. If A can complete a piece of work in $$7\frac{1}{2}$$ hours, then B can do it in ?

Solution(By Examveda Team)

Let time taken by B = x
$${\text{Efficiency}} \propto \frac{1}{{{\text{Time}}\,{\text{taken}}}}$$
So, if B is 100% efficient. then A is 80% efficient
So,
$$\eqalign{ & \Rightarrow \frac{{80}}{{100}} = \frac{x}{{15/2}} \cr & \Rightarrow x = \frac{{80 \times 15}}{{100 \times 2}} \cr & \Rightarrow x = 6\,{\text{hours}} \cr} $$

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Alternate:
Number of hours taken by A to finish the work = $$7\frac{1}{2}$$ hours = $$\frac{15}{2}$$ hours
Work done by A in one hour : $$\frac{2}{15}$$
Let number of hours taken by B to finish the work : $$\frac{1}{{\text{x}}}$$
A can work 20% less than B that is $$\frac{20}{100}$$  = $$\frac{4}{5}$$ times of B’s work.
$$\eqalign{ & {\text{Here,}}\,\frac{4}{5}:1 = \frac{2}{{15}}:\frac{1}{{\text{x}}} \cr & \frac{4}{5} = \frac{{2{\text{x}}}}{{15}} \cr & {\text{x}} = \frac{{15 \times 4}}{{5 \times 2}} = 6\,{\text{hours}} \cr} $$