Multiple choice

Sonia can do a job of printing and typing in 18 days. Raman can do the same work in 54 days and Parmit can do the same work in 108 days. If all the three are working together on the work, the total money to be paid for the work is Rs. 7838. If Sonia gets ill after working for 10 days, then what will be Raman's share?

  1. Rs. 2322.37

  2. Rs. 2412.21

  3. Rs. 2331.45

  4. Rs. 2341.14

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rates: Sonia = 1/18, Raman = 1/54, Parmit = 1/108. In 10 days, Sonia does 10/18 work. Remaining work = 1 - 10/18 = 8/18 = 4/9. Raman and Parmit finish this together. Their combined rate = 1/54 + 1/108 = 3/108 = 1/36. Time taken = (4/9) / (1/36) = 16 days. Total work done by Raman = 16/54 = 8/27. Share = (8/27) * 7838 = 2322.37.

AI explanation

Let the total work be 216 units, making the daily efficiencies of Sonia, Raman, and Parmit 12 units, 4 units, and 2 units respectively. They work together for 10 days, completing 18 units daily for a total of 180 units, leaving 36 units of work. Raman and Parmit complete the remaining work in 36 units divided by their combined rate of 6 units per day, taking 6 days. Raman works for the entire 16 days at 4 units per day to complete 64 units, so his share is 64 divided by 216 of Rs. 7838, which is Rs. 2322.37.

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