ALLIGATION - 02

Question: 300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution? [300 ग्राम चीनी के विलयन में 40% चीनी है. इसमें कितनी चीनी और डाली जाये कि विलयन में चीनी का प्रतिशत बढ़कर 50% हो जाये?]   [Ans. (a) 60 gm]   

(a) 60 gm  (b)65 gm  (c) 50 gm  (d) 55 gm  (e) None of these 

Solution:

Detailed Solution:

First Method: This question is a perfect example of “ALLIGATION”. First of all there is a 300 gram of sugar solution, is which sugar is 40%. So, remaining 60% part is water. If we take Sugar to be added as another solution, then it can be assumed as another solution having composition : sugar = 100% and water = 0%. When the two mixtures are mixed, a new mixture is obtained (mean); in which sugar is 50% and water is also 50%.

The ratio of quantities of mixtures is obtained by method of ‘Alligation’. They are in the ratio of (100-50) : (50-40) or, 50 : 10 or, 5 : 1.

[Initial Solution] 5 ≡ 300 gm

[Sugar added]     1 ≡? = 60 gm Ans.

    

                    By method of Alligation                                                   

                         300 gm                      ?                                           

                     I (S : W)                     II (S : W)                    

                   (40%:60%)               (100%:0%)       

                           40                               100

    

                                Mean (S : W)                   

                                      (50%:50%)

                                              50

                           50 (100-50) :            10 (50-40)                  

                      Or, 5                :              1

                     [Initial Solution] 5 ≡ 300 gm

                     [Sugar added]     1 ≡? = 60 gm Ans.

Second Method: Sugar in the initial solution = 40% of 300 gm = 120 gm and water is 300-120 = 180 gm. Let the quantity of water added is “x” gm.

(120+x)/180  =  50%/50%

(120+x)/180  =  1

X = 60 gm Ans.

Third Method: Sugar in the initial solution = 40% of 300 gm = 120 gm and water is 300-120 = 180 gm. When sugar is added, water in the new solution remains unchanged (that is, 180 gm.), but its percentage changes from 60% to 50%.

Let the quantity of water added is “x” gm.

50% of (300+x) = 180

Or, 300+x = 360

Or, x= 60 gm Ans.