CAT 1994 | Question: 71

Question

A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

• A. 9 : 1
• B. 10 : 1
• C. 11 : 1
• D. None of these

Answer 1

    Let the amount of water added / litre of spirit  =  x

   So now new volume of the mixture                 =  1 + x

   Given S.P. of the mixture                               =  Rs 75 per litre

   Hence total S.P.                                            =  75(1+x)

   Whereas  C.P.                                               =  60 [  As no cost for water mentioned ]

   Hence profit                                                   =  75 + 75x - 60   =   75x + 15

   Hence profit percentage                                 =   (Profit / C.P) * 100    =  [15(5x + 1) / 60] * 100

   Given profit percentage                                  =   37.5 %

   Hence we have ,

                                [15(5x + 1) / 60] *  100     =    37.50

                    ==>      (5x + 1) / 4                      =    0.375

                    ==>       5x + 1                           =    1.50

                    ==>       x                                   =    0.1

  Hence for each litre of spirit , 0.1 litre of water is added to get the desired mixture.

  Hence the ratio of spirit to water in the mixture           =     1 : 0.1     =    10 : 1

  Hence B) should be the correct answer.