Question : A is 20% more efficient than B. How much time will they working together take to complete a job which A alone could have done in 29 days?
Option 1: $\frac{145}{11}$ days
Option 2: $\frac{116}{11}$ days
Option 3: $\frac{203}{11}$ days
Option 4: $\frac{174}{11}$ days
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Correct Answer: $\frac{174}{11}$ days
Solution : According to the question, The efficiency of A is 20% more than that of B Let the efficiency of B be 100% $\therefore$ The efficiency of A = 120% of the efficiency of B ⇒ Efficiency of A = $\frac{6}{5}$ of efficiency of B ⇒ $\frac{\text{Efficiency of A}}{\text{Efficiency of B}} = \frac{6}{5}$ Now, Total work = Efficiency of A $\times$ Time taken by A $=6× 29 =174$ Now, Total efficiency = $5 + 6=11$ Time taken by (A + B) to complete the whole work =$\frac{\text{Total work}}{\text{Total efficiency}}$ $=\frac{174}{11}$ days Hence, the correct answer is $\frac{174}{11}$ days.
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