ALLIGATION - 01

Question: A mixture of a certain quantity of milk with 16 liters of water is worth 90 P/ liter. If pure milk be worth 108 P per litre how much milk is there in the mixture? [जब 16 लीटर पानी में दूध की एक विशेष मात्रा मिलायी जाती है, तो मिश्रण की दर 90 पैसे/लीटर हो जाती है. यदि शुद्ध दूध 108 पैसे/लीटर हो, तो मिश्रण में दूध की मात्रा बताएँ] [Ans. (a) 80 ]

(a) 80 liters  (b) 60 liter  (c) 90 liters (d) 75 liters  (e) None of these

Detailed Explanation: The quantity of water is 16 liters and a certain quantity of milk is to be added to this. What quantity of milk is added, is to be determined.

In the method of “Alligation” rates of the two mixtures (the mixtures which are to be mixed) should be given and the mixture of these two mixtures (mean value) should also be given.

Here, the rate of pure milk is 108 P/L, whereas the rate of water added is always taken as 0 P/L. Given that the rate of the mixture (mixture of pure milk and water) is given as 90 P/L.

 

                          By method of Alligation 

                                                   

                         16 liters                     ?                                           

                     Water P/L)                Milk (P/L)                    

                          0                             108    

                                    Mean (P/L)                   

                                         90                                         

                         18 (108-90) :          90 (90-0)                  

                    Or, 1                :           5

                                    1 ≡ 16 liters

                                    5 ≡? = 80 liters Ans.

  

The ratio of quantities of water and milk is, (108 – 90) : (90 - 0)

That is, 18 : 90 means, 1 : 5

   

Quantities of water is 1 ≡ 16 liters

Quantities of milk is  5 ≡ ? = 80 liters Ans.