Multiple choice

Raman alone can complete a job in 16 days. Frank alone can complete the same job in 24 days. Raman, Frank and Ricky together complete the job in 8 days and get paid a total of Rs. 4000 for it. Find Raman's share (in Rs.).

  1. 2000

  2. 1000

  3. 4000

  4. 1333.33
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Raman's rate = 1/16, Frank's rate = 1/24. Combined rate of Raman and Frank = 1/16 + 1/24 = 5/48. Together with Ricky, they complete the job in 8 days (rate = 1/8). Ricky's rate = 1/8 - 5/48 = 1/48. The work done by each in 8 days: Raman = 8/16 = 1/2, Frank = 8/24 = 1/3, Ricky = 8/48 = 1/6. Raman's share = (1/2) * 4000 = 2000.

AI explanation

Raman and Frank finish the job in 16 and 24 days, so their combined daily work is 1/16 + 1/24 = 5/48. All three together complete it in 8 days, meaning their combined rate is 1/8 or 6/48. Subtracting Raman and Frank's rate from the total gives Ricky's rate as 6/48 - 5/48 = 1/48. The Rs. 4000 payment is split in the ratio of their efficiencies: 1/16 : 1/24 : 1/48. Multiplying by 48, this ratio becomes 3 : 2 : 1. Raman's share is 3/6 of the total Rs. 4000, which equals Rs. 2000.

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