Correct Answer - Option 4 : 43.75 days
Given:
A and B can complete the work in 35 days
and if A works double his efficiency and B works 1/3
(33.33% = 1/3), the work will be completed in 21 days.
Formula Used:
Total work = Efficiency × Time
Note: We will equalize both the equations in these type of
questions to obtain efficiencies.
Calculation:
We will find efficiencies by trying to equate
both the conditions:
(A + B) × 35 = (2A + (B/3)) × 21
⇒ 5A + 5B = 6A + B
⇒ 4B = A
⇒ A/B = 4/1 (required ratios of efficiency)
Now, Total Work = (A + B) × 35 units
So, Total Work = (1 + 4) × 35 units
⇒ 5 × 35 = 175
Time required by A to complete the whole work
⇒ Total Work/Efficiency of A
⇒ 175/4 days
⇒ 43.75 days
∴ The time taken by A to complete the work is 43.75 days