Question : A is 50% more efficient than B. B finished the same work in 20 days. If A and B worked together, then how much time would they take to finish the same work?
Option 1: 10 days
Option 2: 7 days
Option 3: 8 days
Option 4: 9 days
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Correct Answer: 8 days
Solution :
Let the efficiency of B be 100.
So, the efficiency of A = 100 + 50 =150
The efficiency ratio of A and B = 150 : 100 = 3 : 2
Total efficiency = 3 + 2 = 5 units
The time taken by B to finish the work is 20 days.
So, Total work = Efficiency of B × Time taken by B
⇒ Total work = 2 × 20 = 40 units
Time taken by (A + B) to complete the work
= $\frac{\text{Total work}}{\text{Total efficiency}}$
= $\frac{40}{5}$
= $8$ days
A and B together will finish the work in 8 days.
Hence, the correct answer is 8 days.
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