ALLIGATION - 03

Question: The milk and water in two vessels A and B are in the ratio of 4:3 and 2:3 respectively. In what ratio the liquids in both the vessels are mixed to obtain a new mixture in vessel C containing half milk and half water? [दो पात्रों A तथा B में दूध एवं पानी का अनुपात क्रमशः 4:3 तथा 2:3 है. दोनों पात्रों के द्रवों को एक नए पात्र C में किस अनुपात में मिलाया जाये कि उसमें आधा दूध तथा आधा पानी हो जाये?] [Ans. (a) 7:5]

(a) 7:5   (b) 5:2   (c) 3:11  (d) 1:2   (e) None of these

Solution:

Detailed Explanation: This question is a perfect example of the method of “Alligation”. The milk and water in two vessels A and B are in the ratio of 4:3 and 2:3 respectively; whereas this ratio in the mixture of the liquids in vessel C is 1:1.

In the method of Alligation, the rate is taken. Rate may be in per hundred (percent), per thousand or in parts. Here the rate “parts” is more comfortable. The part of any liquid – “milk” or “water”- can be taken. If parts of milk is taken, then milk is 4/7^th the part in the first vessel, and 2/5^th part in the second vessel; whereas ½ part in the mixture of liquids in vessel C.

The ratio of the liquids in two vessels A and B are (1/2-2/5): (4/7-1/2), or, 1/10: 1/14. 

Or, 14:10, or, 7: 5   Ans.

                  By method of Alligation 

                                                  

                         I (M: W)              II (M: W)                    

                             (4: 3)                      2: 3)       

                               4/7                        2/5

                                   Mean (S: W)                   

                                              (1: 1)

                                                1/2

                            (1/2-2/5)      :     (4/7-1/2)                  

                             Or, 1/10     :      1/14

                             Or, 14        :       10

                               Or, 7        :         5   Ans.