A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

Explanation:-

$$\eqalign{ & {\text{Ratio}}\,{\text{of}}\,{\text{times}}\,{\text{taken}}\,{\text{by}}\,{\text{A}}\,{\text{and}}\,{\text{B}} \cr & = 100:130 = 10:13 \cr & {\text{Suppose}}\,{\text{B}}\,{\text{takes}}\,x\,{\text{days}}\,{\text{to}}\,{\text{do}}\,{\text{the}}\,{\text{work}} \cr & {\text{Then}},10:13::23:x \cr & \Rightarrow x = \left( {\frac{{23 \times 13}}{{10}}} \right) \cr & \Rightarrow x = \frac{{299}}{{10}} \cr & {\text{A's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{1}{{23}} \cr & {\text{B's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = \frac{{10}}{{299}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = \left( {\frac{1}{{23}} + \frac{{10}}{{299}}} \right) \cr & = \frac{{23}}{{299}} \cr & = \frac{1}{{13}} \cr & \therefore A\,{\text{and}}\,{\text{B}}\,{\text{together}}\,{\text{can}}\,{\text{complete}} \cr & \,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{13}}\,{\text{days}}{\text{.}} \cr}$$