Question : A is 40% more efficient than B. How much time will they take to work together to complete a job which A alone could have done in 31 days?
Option 1: $\frac{217}{12}\ \text{days}$
Option 2: $\frac{515}{32}\ \text{days}$
Option 3: $\frac{215}{12}\ \text{days}$
Option 4: $\frac{517}{32}\ \text{days}$
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Correct Answer: $\frac{217}{12}\ \text{days}$
Solution : Given: A is 40% more efficient than B. The time taken by A to complete the task alone is 31 days. Work = Time × Efficiency. Let B's efficiency be 100. Then, $\frac{A}{B} = \frac{140}{100}$ ⇒ $\frac{A}{B} = \frac{7}{5}$ The total work is done by A in 31 days. Let the total work = 31 × 7 = 217 units So, the time taken with A and B working together $=\frac{217}{7+5}=\frac{217}{12}$ days Hence, the correct answer is $\frac{217}{12}\ \text{days}$.
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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
Question : A alone can do $\frac{2}{5}$ of a work in 12 days. B is 25% more efficient than A. C alone can do the same work in 12 days less than B. D is 25% less efficient than C. If they all work together, then the work will be completed in how many days?
Option 1: $\frac{240}{53}$ days
Option 2: $\frac{180}{43}$ days
Option 3: $\frac{200}{51}$ days
Option 4: $\frac{300}{47}$ days
Question : If Anju is 30% more efficient than Bittu, then how much time will they take, working together, to complete a job which Anju alone could have done in 23 days?
Option 1: $13$ days
Option 2: $20 \frac{3}{17}$ days
Option 3: $15$ days
Option 4: $11$ days
Question : Rekha alone can complete a task in 16 days and Bina alone can complete the same task in 12 days. Starting with Rekha, they work on alternate days. The task will be completed in:
Option 1: $12 \frac{3}{4}\ \text{days}$
Option 2: $12\ \text{days}$
Option 3: $13\ \text{days}$
Option 4: $13 \frac{3}{4}\ \text{days}$
Question : A is 40% more efficient than B. How much time will both, working together, take to finish the work, which B alone can finish in 36 days?
Option 1: $18$ days
Option 2: $9 \frac{1}{3}$ days
Option 4: $11 \frac{2}{3}$ days
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