Manoj is twice as efficient a fisherman as Anuraj, and together they complete a piece of work in 22 days. In how many days can Anuraj alone complete the same work?
Efficiency Calculation for Anuraj Alone
Let the rate at which Anuraj works be '$R_A$' units per day.
Manoj is twice as efficient as Anuraj. Therefore, Manoj's work rate is '$R_M = 2 \times R_A$' units per day.
When they work together, their combined work rate is the sum of their individual rates:
$ R_{combined} = R_M + R_A = (2 R_A) + R_A = 3 R_A $
They complete the work together in 22 days. The total amount of work ($W$) can be calculated as:
$ W = R_{combined} \times \text{Time taken together} $
$ W = (3 R_A) \times 22 \text{ days} = 66 R_A \text{ units} $
To find the number of days Anuraj alone can complete the same work, we use the formula:
$ \text{Time for Anuraj} = \frac{\text{Total Work}}{\text{Anuraj's Work Rate}} $
$ \text{Time for Anuraj} = \frac{W}{R_A} = \frac{66 R_A \text{ units}}{R_A \text{ units/day}} $
$ \text{Time for Anuraj} = 66 \text{ days} $
Therefore, Anuraj alone can complete the same work in 66 days.
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Important Questions from Work Efficiency
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