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In a team of 2 women Anita and Shivika, the former is 12.5% more efficient than the latter and completes a task in 37 hours. They both start the task together, but Anita faints after working for 15 hours and the rest of the task is completed by Shivika alone at 1/4 times her efficiency. Find the total time in which this team will complete the task.

In a team of 2 women Anita and Shivika, the former is 12.5% more efficient than the latter and completes a task in 37 hours. They both start the task together, but Anita faints after working for 15 hours and the rest of the task is completed by Shivika alone at 1/4 times her efficiency. Find the total time in which this team will complete the task. Correct Answer 54 hrs

Given:

Difference between efficiencies of 2 women = 12.5%

Time taken by Anita to complete the task = 37 hrs

Time for which both works = 15 hrs

Formula Used:

Total Work = Efficiency × Time

Calculations:

Let the efficiencies of Anita and Shivika be x and y respectively.

Let the time in which Shivika completes rest of the task be t hours.

Anita is 12.5% more efficient than Shivika

⇒ x : y = (100 + 12.5) : 100

⇒ x : y = 9 : 8

Total Work = Efficiency of Anita × Time taken by Anita

⇒ Total work = 9 × 37

⇒ Total work = 333      ----(1)

Work done by both in 15 hrs = 15 × (x + y)

Efficiency of Shivika complete left work = y/4

⇒ Rest work done by Shivika = (y/4) × d

Total Work = 25 × (x + y) + (y/4) × t      ----(2)

Equating (1) and (2), we get

⇒ 15 × (x + y) + (y/4) × t = 333

⇒ 15 × (9 + 8) + (8/4) × t = 333

⇒ 255 + 2t = 333

⇒ t = 78/2 = 39 hrs

Total time taken to complete the task = 15 hrs + 39 hrs

⇒ Total time taken to complete the task = 54 hrs

∴ The total time in which this team will complete the task is 54 hrs.

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