Mixtures

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Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.


1. In what ratio must water be mixed with milk costing Rs.12 per liter to obtain a mixture worth of Rs.8 per liter?

A. 3:2

B. 1:2

C. 2:3

D. 2:1


Answer

                  Ans: Option B

       Explanation:

       12 – 8: 8 – 0 = 1 : 2


2. In what ratio must water be mixed with milk to gain 1623% on selling the mixture at cost price?

A. 6: 1

B. 1: 6

C. 1: 4

D. 4: 1


Answer

                  Ans: Option B

       Explanation:       ​

       Answer: Option B

       Explanation:

       Let CP of 1 liter milk = Rs.1

       SP of 1 liter mixture = CP of 1 liter milk = Rs.1Gain

       =1623%=503%CP of 1 liter mixture

       = 100(100+Gain %) ×SP=100(100+503)×1=100(3503)=300350=67

       By the rule of allegation, we have

       CP of 1 liter water                                                                                                            CP of 1 liter milk

               0                                                                                                                                       1

                                                                   CP of 1 liter mixture

                                                                       6/7

 

       1 – 6/7 = 1/7                                                                                                                          6/7 – 0 = 6/7

      Quantity of water: Quantity of milk = 1/7 : 6/7 = 1 : 6


3. A bag contains 57 kg of rice with 7.5% contamination. How many kg of non-contaminated rice should be added to the bag so that the resultant mixture contains 6% contamination?

A. 14.25 kg

B. 15 kg

C. 14 kg

D. 14.5 kg


Answer

                  Ans: Option A

       Explanation:

       ​Amount of contamination in the bag = 7.5% of 57 = 7.5*57/100

       Let x kg of pure rice be added to the bag.

       (7.5*57/100) ÷ (57+x) = 6/100 x = 14.25 kg


4. A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

 A. 4%

B.6 %

C.20%

D.25%


Answer

                  Ans: Option C

       Explanation:

       Let C.P. of 1 liter milk be Re. 1

       Then, S.P. of 1 liter of mixture = Re. 1, Gain = 25%.

       C.P. of 1 liter mixture = Re.   (100/125) x 1   = 4/5

       By the rule of allegation, we have:

       C.P. of 1 liter of milk                                                                                      C.P. of 1 liter of water

       Re. 1 Mean Price                                      Mean Price                                                         0

                 4                                                             4                                                              1

                 5                                                             5                                                              5

       Ratio of milk to water = 4/5: 1/5 = 4: 1.

      Hence, percentage of water in the mixture =   (1/5) x 100% = 20%.​


5. The milk and water in two vessels A and B are in the ratio 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 consisting half milk and half water?

A. 4:3

B. 2:3

C. 7:5

D. 8:3


Answer

                  Ans: Option C

       Explanation:

       Milk in 1 liter mixture of A = 4/7 liter.

       Milk in 1 liter mixture of B = 2/5 liter.

       Milk in 1 liter mixture of C = 1/2 liter.

       By rule of allegation we have required ratio X:Y

       X                  :                 Y

       4/7                                2/5

 

           \                      /

            (Mean ratio)

                  (1/2)

           /                      \

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

      1/10                      1/1 4

      So Required ratio = X: Y = 1/10 : 1/14 = 7:5


6. In 1 kg mixture of iron and manganese 20% of manganese. How much iron should be added so that the proportion of manganese becomes 10%

A. 1.5 Kg

B. 2 Kg

C. .5 Kg

D. 1 Kg


Answer

                  Ans: Option D

       Explanation:

       By the rule of allegation, we have

       Percentage concentration of                                                                      Percentage concentration of

       Manganese in the mixture: 20                                                                   Manganese in the mixture: 0                                                                     

                                                             Percentage concentration of

                                                             manganese in the final mixture 10

 

         10 – 0 = 10                                                                                                           20 – 10 = 10

       Quantity of the mixture: Quantity of iron = 10: 10 = 1 : 1

       Given that Quantity of the mixture = 1 Kg

       Hence Quantity of iron to be added = 1 Kg


7. Rahari dal costs Rs.75/kg. Musuri dal which is used as a supplement for Rahari dhal costs Rs.60/kg. A family needs a total of 10 kg of dhal and they spend Rs.660 to buy a few kg of Rahari and musuri. How many kg of Rahari dal and musuri dal have they bought?

A. 4, 6

B. 6, 4

C. 5, 5

D. 3, 7


Answer

                  Ans: Option A

       Explanation:

      Let the quantity of Rahari dal bought be x kg.

      Then, musuri dal = (10-x)kg

      75x+60(10-x) = 660

       X = 4 ​


8. Two vessels A and B contain milk and water mixed in the ratio 8: 5 and 5 : 2 respectively. The ratio in which these two mixtures be mixed to get a new mixture containing milk and water in the ratio 9: 4?

 A. 2:7

 B. 3:5

 C. 5:2

 D. 5:7


Answer

                  Ans: Option A

       Explanation:

       No explanation​


9. How many kg of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kg of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?

A. 16 kg

B. 12.5 kg

C. 200 kg

D. 20 kg


Answer

                  Ans: Option D

       Explanation:

       Let the amount of Basmati rice being mixed be x kg.

       As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture = Rs.32/kg.

       i.e. (x×42)+(25×24)=32(x+25)

       42x+600=32x+800

       10x=200

        x=20 kg.


10. The cost of Type 1 rice is Rs.15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:

 A.Rs. 18

B.Rs. 18.50

C.Rs. 19

D.Rs. 19.50


Answer

                  Ans: Option A

       Explanation:

       Let the price of the mixed variety be Rs.x per kg.

       By rule of allegation, we have:

      Cost of 1 kg of Type 1 rice                                                        Cost of 1 kg of Type 2 rice

       Rs.15                                                     Mean Price                              Rs.20

                                                            Rs.x

      (20 – x )                                                                                               (x – 15)

      (20 – x )/ (x – 15)= 2/3

      60 – 3x = 2x – 30

      5x = 90

      X = 18.


11. The proportion of milk and water in 3 samples is 4:3, 5:2 and 2:1. A mixture comprising of equal quantities of all 3 samples is made. The proportion of milk and water in the mixture is

A. 11:6

B. 41:21

C. 21:11

D. 41:22


Answer

                  Ans: Option D

       Explanation:

       ​Let us consider 1 liter of each sample.

      Proportion of milk = (4/7) + (5/7) + (2/3) = 41/21

      Proportion of water = (3/7) + (2/7) + (1/3) = 22/21

      Proportion of milk and water = 41:22


12. A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is

 A. 640 kg

 B. 600 kg

 C. 560 kg

 D. 400 kg


Answer

                  Ans: Option B

       Explanation:

       Ratio of first and second part = 4: 6 = 2: 3

       Quantity of 2 kind = (1000*3/5) = 600 Kg


13. A can contains a mixture of two liquids A and B is the ratio 7: 5. When 9 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7: 9. How many liters of liquid A were contained by the can initially?

 A.10

B.20

C.21

D.25


Answer

                  Ans: Option C

       Explanation:

        Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

        Quantity of A in mixture left =   7x – (7/12) x 9   liters =   7x – (21/4)   liters.

        Quantity of B in mixture left =   5x – (5/12) x 9   liters =   5x – (15/14)   liters.

        {[7x – (21/4)] / [5x – (15/4)]} + 9 = 7/9

        (28x – 21)/ (20x + 21) = 7/9

        252x – 189 = 140x + 147

        112x = 336

         X = 3.

       So, the can contained 21 liters of A.


14. Two glasses A and B contain a mixture of water and honey in the ratio 5:1 and 4:1 respectively. One-fourths of the mixture in glass A is poured out and refilled with the mixture from glass B. Find the ratio of water and honey in glass A.

A. 20:1

B. 33:7

C. 10:1

D. 22:3


Answer

                  Ans: Option B

       Explanation:

       ​The resulting mixture contains A and B in the ratio 3:1(three-fouths of A and one-fourths of B.

       Proportion of water = [3*(5/6)+1*(4/5)]/(3+1) = 33/40

       Proportion of honey = [3*(1/6)+1*(1/5)]/(3+1) = 7/40

       Water and Honey = 33:7


15. We have a 630 ml of mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?

A. 70 ml

B. 60 ml

C. 80 ml

D. 50 ml


Answer

                  Ans: Option A

       Explanation:

        Concentration of water in mixture1 = 2/9 (Since the ratio of milk and water = 7:2) —item (1)

        Concentration of water in pure water= 1 —item (2)

        Now the above mentioned items are mixed to form a mixture2 where milk and water ratio = 7: 3

        Concentration of water in mixture2 = 3/10

        By the rule of allegation, we have

        Concentration of water                                                                                                                 Concentration of water

         In mixture 1: 2/9                                                                                                                                in pure water: 1

 

                                                                Mean concentration

                                                                           3/10

           1 – 3/10 = 7/10                                                                                                                                   3/10 – 2/9 = 7/90

         Quantity of mixture1: Quantity of water = 7/10: 7/90 = 1/10: 1/90 = 1 : 1/9

          Given that Quantity of mixture1 = 630 ml

          630: Quantity of water = 1: 1/9

          Quantity of water = 630×19=70 ml


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