Quantitative Aptitude: Mixture and Alligation Set 1

Mixture and Alligation Questions for the upcoming exams like IBPS PO, SBI PO, IPPB, LIC, RBI, Manipal University Course exams etc.

1. A 56 litre mixture contains milk and water in the ratio of 5 : 2 . How much water should be added to the mixture so as make the resultant mixture containing 40% water in it?
   A) 35/6 l
   B) 40/3 l
   C) 29/3 l
   D) 27/2 l
   E) 32/3 l
   
   View Answer

   Option E
   Solution:
   In 56 l, milk = 5/(5+2) * 56 = 40 l, so water = 56 – 40 = 16 l
   Final ratio of milk to water will be = 60 : 40 = 3 : 2
   Let x litres of water to be added. So
   40/(16+x) = 3/2
   Solve, x = 32/3 l
2. A mixture of 30 litres contains milk and water in the ratio 7 : 3. 10 litres of the mixture is taken out and replaced with pure milk and the same operation is repeated one more time. Find the final ratio of milk to water in the mixture.
   A) 12 : 7
   B) 9 : 4
   C) 13 : 2
   D) 15 : 7
   E) 11 : 5
   
   View Answer

   Option C
   Solution:
   In 30 l of mixture, milk = 7/10 * 30 = 21l, so water = 9 l
   let x = amount of water after replacement and y = amount of water before replacement, so y = 9
   Now
   x/y = [1 – 10/30]²
   Solve, x = 4 l
   Now since mixture is 30 l only after replacement also. So milk in mixture after replacement = 30 – 4 = 26 l
   So final ratio = 26 : 4 = 13 : 2
   
3. How much milk (in litres) costing Rs 50 per litres should be mixed with 18 litres of milk costing Rs 56 per litres so that there is a profit of 25% on selling the mixture at Rs 65 per litres?
   A) 25 l
   B) 32 l
   C) 17 l
   D) 36 l
   E) 46 l
   
   View Answer

   Option D
   Solution:
   CP of mixture = 100/125 * 65 = Rs 52
   Let x l of milk to be mixed. So by method of allegation:
   (x)……………..…..(18)
   50…………………..56
   ………….52
   4……………………..2
   So x/18 = 4/2
   x = 36 l
4. A 24 litres of milk and water mixture contains milk and water in the ratio 3 : 5. What litres of the mixture should be taken out and replaced with pure milk so that the final mixture contains milk and water in equal proportions?
   A) 22/3 l
   B) 20/3 l
   C) 3 l
   D) 32/5 l
   E) 24/5 l
   
   View Answer

   Option E
   Solution:
   In 24 l of mixture, milk = 3/8 * 24 = 9 l, so water = 15 l
   Now since the mixture is to be replaced with pure milk, the amount of mixture will remain same after replacement too.
   In 24 l mixture, to have 12 l water and 12 l milk, 3 l of water should be taken out, since we are only adding milk.
   Let x l of mixture taken out. So 5/8 * x = 3,
   Solve, x = 24/5 l
5. 25 litres are drawn from a cask full of wine and is then filled with water. This operation is performed one more time. The ratio of the quantity of wine now left in cask to that of the water is 36 : 85. How much wine the cask hold originally?
   A) 66 l
   B) 85 l
   C) 59 l
   D) 55 l
   E) 46 l
   
   View Answer

   Option D
   Solution:
   Let x l wine was there originally. So
   36/(36+85) = (1 – 25/x)²
   Solve, x = 55 l
6. Out of 2100 kg wheat, some part is sold making 10% profit while the remaining part is sold making 16% profit. If there is an overall profit of 14%, what quantity was sold at 16% profit?
   A) 700 kg
   B) 1300 kg
   C) 1400 kg
   D) 1000 kg
   E) 1100 kg
   
   View Answer

   Option C
   Solution:
   By method of Alligation:
   10………………..16
   …………14
   (16-14)…………..(14-10)
   2……………….4
   So 2 : 4 = 1 : 2
   so part at 16% profit = 2/(1+2) * 2100 = 1400 kg
7. Container A and B contains water and alcohol in the ratio 1 : 3 and 3 : 2 respectively. How much amount of mixture from container A should be mixed with 30 l of mixture from container B, so that the resultant mixture contains water and alcohol in the ratio 11 : 12?
   A) 26 l
   B) 16 l
   C) 22 l
   D) 15 l
   E) None of these
   
   View Answer

   Option B
   Solution:
   Water in A = 1/4. Water in B = 3/5 . And in resultant =11/23
   So by allegation method:
   (x)…………….(30)
   1/4………………..3/5
   ………..11/23
   14/(23*5)…………..21/(23*4)
   Take ratio: 14/23*5 : 21/23*4
   Gives 8 : 15
   So x/30 = 8/15
   Solve, x = 16 l
8. The rice sold by a shopkeeper contains 15% low quality rice. What quantity of good quality rice should be added to 70 kg of rice so that percentage of low quality wheat becomes 7%?
   A) 50 kg
   B) 40 kg
   C) 90 kg
   D) 60 kg
   E) 80 kg
   
   View Answer

   Option E
   Solution:
   In good quality rice, there is 0% low quality rice
   So method of allegation:
   (70 kg)……………………(x kg)
   15% …………………………0%
   …………………..7%
   7……………………………..8
   So 7 : 8
   Gives 70/x = 7/8
   Solve, x = 80 kg
   
9. Container A and B contains 25% and 50% water respectively. The rest is milk in both the containers. How much amount should be mixed from container A to some amount in to some amount of container B so as to get 12 litres of new mixture having water to milk ratio 3 : 5?
   A) 6 l
   B) 8 l
   C) 10 l
   D) 7 l
   E) 5 l
   
   View Answer

   Option A
   Solution:
   In resultant mixture, water is 3/8 * 100 = 75/2%
   So by method of allegation:
   25%……………………………50%
   ………………..75/2%
   25/2%……………………….25/2%
   so ratio is 25/2 : 25/2 = 1 : 1
   And the total should be 12 l, so 6 l of mixture from A, and 6 l from B.
10. A mixture contains A and B in the ratio of 5 : 3. 16 litres of this mixture is taken out and 5 litres of A is poured in. the new mixture has ratio of A to B as 11 : 6. Find the total original quantity of mixture.
    A) 80 litres
    B) 96 litres
    C) 98 litres
    D) 84 litres
    E) 92 litres
    
    View Answer
    Option B
    Solution:
    A = 5x, B = 3x
    16 l taken out, so let total mixture now = 5x + 3x + 16 = 8x + 16
    Now 5 l of A poured in and then ratio becomes 11 : 6
    So (5x+5)/3x = 11/6
    Solve, x = 10
    So total mixture originally = 8x + 16 = 8*10 + 16 = 96 litres
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