Question
A man completes $$\frac{5}{8}$$ of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
Answer: Option B
$$\eqalign{
& {\text{Work}}\,{\text{done}} = \frac{5}{8} \cr
& {\text{Balance}}\,{\text{work}} = {1 - \frac{5}{8}} = \frac{3}{8} \cr
& {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{number}}\,{\text{of}}\,{\text{days}}\,{\text{be}}\,x \cr
& {\text{Then}}, \cr
&\frac{5}{8}:\frac{3}{8} :: 10:x \cr
& \Rightarrow \frac{5}{8} \times x = \frac{3}{8} \times 10 \cr
& \Rightarrow x = {\frac{3}{8} \times 10 \times \frac{8}{5}} \cr
& \Rightarrow x = 6 \cr} $$
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$$\eqalign{
& {\text{Work}}\,{\text{done}} = \frac{5}{8} \cr
& {\text{Balance}}\,{\text{work}} = {1 - \frac{5}{8}} = \frac{3}{8} \cr
& {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{number}}\,{\text{of}}\,{\text{days}}\,{\text{be}}\,x \cr
& {\text{Then}}, \cr
&\frac{5}{8}:\frac{3}{8} :: 10:x \cr
& \Rightarrow \frac{5}{8} \times x = \frac{3}{8} \times 10 \cr
& \Rightarrow x = {\frac{3}{8} \times 10 \times \frac{8}{5}} \cr
& \Rightarrow x = 6 \cr} $$
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