Ravi and Ramu are partners in a business.Ravi contributes 1/6 of the capital for 16 months and Ramu received 2/3 of the profit. For how long Ramu's money was used?

a)8 months b)12 months c)15 months d)17 months

• Let the total Profit be Z.
  Ramu's profit share is 2/3 of profit (i.e 2Z/3)
  Ravi's profit is (Z-2Z/3) =Z/3
  Hence the profit ratio is , Ravi : Ramu = Z/3 : 2Z/3 = 1:2
  
  Let total Capital be Rs.X and Ramu has contributed for Y months.Since Ramu's profit share is 2/3, his invest share will be 2/3 in capital.
  
  Ravi's invest for 16 months / Ramu's invest for Y months = Ravi's profit share / Ramu's profit share
  i.e. (X/6 x 16) / (2X/3 x Y) = 1/2
  
  Solving the above equation, we get Y = 8.
  So Ramu's money has been used for 8 months.
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