Directions (1-5): Study the following information carefully and answer the questions give below:

The following table contains information about seven mixtures. Some data in the table are missing.

1) Quantity of milk in the final mixture A is what percent of amount of water in the final mixture B?

a) 85.5%

b) 72.5%

c) 112.5%

d) 98.5%

e) None of these

2) Find the respective ratio of amount of milk in final mixture C and amount of water in final mixture D.

a) 5:2

b) 4:3

c) 3:1

d) 3:2

e) None of these

3) Another mixture H contains amount of milk equal to 20% more than the amount of milk in the final mixture E and water equal to 40% more than the amount of water in the final mixture E. Find the difference between total quantity of mixture H and final quantity of mixture E.

a) 12 litres

b) 14 litres

c) 15 litres

d) 18 litres

e) None of these

4) Find the sum of the quantities of milk in all the final mixtures.

a) 515 litres

b) 415 litres

c) 325 litres

d) 225 litres

e) None of these

5) A mixture K contains amount of milk equal to 25% more than the amount of milk in final mixture G and amount of water equal to 10% less than the amount of water in the final mixture C. The milkman sold 34 litres of the mixture and added 10 litres of milk and 12 litres of water to the remaining mixture. Find the difference between quantity of milk and quantity of water in the final mixture K.

a) 25 litres

b) 30 litres

c) 40 litres

d) 50 litres

e) None of these

Answers :

 

1) Answer: c)

Quantity of milk in the remaining mixture A = 7/12 x 60 = 35 litres

Quantity of water in the remaining mixture A = 5/12 x 60 = 25 litres

Let, the amount of milk added to the remaining mixture A = n litres

(35 + n)/(25 + 5) = 3/2

=> 2 x (35 + n) = 3 x 30

=> 70 + 2n = 90

=> 2n = 90 – 70

=> 2n = 20

=> n = 20/2

=> n = 10 litres

Quantity of milk in the final mixture A = 35 + 10 = 45 litres

Quantity of milk in the remaining mixture B = 5/9 x 81 = 45 litres

Quantity of water in the remaining mixture B = 4/9 x 81 = 36 litres

Let the amount of water added to the remaining mixture B = k litres

(45 + 5)/(36 + k) = 5/4

=> 4 x 50 = 5 x (36 + k)

=> 200 = 180 + 5k

=> 5k = 200 – 180

=> 5k = 20

=> k = 4 litres

Quantity of water in the final mixture B = 36 + 4 = 40 litres

Required percentage = 45/40 x 100 = 112.5%

2) Answer: c)

Remaining mixture C = 96 – 24 = 72 litres

Quantity of milk in the remaining mixture C = 5/8 x 72 = 45 litres

Quantity of water in the remaining mixture C = 3/8 x 72 = 27 litres

Let the amount of milk added to the remaining mixture = l litres

(45 + l)/(27 + 3) = 2/1

=> 45 + l = 2 x 30

=> l = 60 – 45

=> l = 15 litres

Quantity of milk in the final mixture C = 45 + 15 = 60 litres

Remaining mixture D = 78 – 39 = 39 litres

Quantity of milk in the remaining mixture D = 7/13 x 39 = 21 litres

Quantity of water in the remaining mixture D = 6/13 x 39 = 18 litres

Let, the amount of water added to the remaining mixture D = m litres

(21 + 9)/(18 + m) = 3/2

=> 2 x 30 = 3 x (18 + m)

=> 60 = 54 + 3m

=> 3m = 60 – 54

=> 3m = 6

=> m = 2

Amount of water in the final mixture D = 18 + 2 = 20 litres

Required ratio = 60: 20 = 3:1

3) Answer: b)

Amount of milk in the remaining mixture E = 4/7 x 28 = 16 litres

Amount of water in the remaining mixture E = 3/7 x 28 = 12 litres

Let the amount of milk added to the remaining mixture E = p litres

(16 + p)/(12 + 8) = 3/2

=> 2 x (16 + p) = 20 x 3

=> 32 + 2p = 60

=> 2p = 60 – 32

=> 2p = 28

=> p = 28/2

=> p = 14 litres

Amount of milk in the final mixture E = 16 + 14 = 30 litres

Amount of water in the final mixture E = 12 + 8 = 20 litres

Total amount of final mixture E = 30 + 20 = 50 litres

Amount of milk in mixture H = 30 x 120/100 = 36 litres

Amount of water in mixture H = 20 x 140/100 = 28 litres

Total amount of mixture H = 36 + 28 = 64 litres

Required difference = 64 – 50 = 14 litres

4) Answer: c)

Quantity of milk in the remaining mixture A = 7/12 x 60 = 35 litres

Quantity of water in the remaining mixture A = 5/12 x 60 = 25 litres

Let, the amount of milk added to the remaining mixture A = n litres

(35 + n)/(25 + 5) = 3/2

=> 2 x (35 + n) = 3 x 30

=> 70 + 2n = 90

=> 2n = 90 – 70

=> 2n = 20

=> n = 20/2

=> n = 10 litres

Quantity of milk in the final mixture A = 35 + 10 = 45 litres

Quantity of milk in the remaining mixture B = 5/9 x 81 = 45 litres

Quantity of milk in the final mixture B = 45 + 5 = 50 litres

Remaining mixture C = 96 – 24 = 72 litres

Quantity of milk in the remaining mixture C = 5/8 x 72 = 45 litres

Quantity of water in the remaining mixture C = 3/8 x 72 = 27 litres

Let the amount of milk added to the remaining mixture = l litres

(45 + l)/(27 + 3) = 2/1

=> 45 + l = 2 x 30

=> l = 60 – 45

=> l = 15 litres

Quantity of milk in the final mixture C = 45 + 15 = 60 litres

Remaining mixture D = 78 – 39 = 39 litres

Quantity of milk in the remaining mixture D = 7/13 x 39 = 21 litres

Quantity of milk in the final mixture D = 21 + 9 = 30 litres

Quantity of milk in the remaining mixture E = 4/7 x 28 = 16 litres

Quantity of water in the remaining mixture E = 3/7 x 28 = 12 litres

Let the amount of milk added to the remaining mixture E = p litres

(16 + p)/(12 + 8) = 3/2

=> 2 x (16 + p) = 20 x 3

=> 32 + 2p = 60

=> 2p = 60 – 32

=> 2p = 28

=> p = 28/2

=> p = 14 litres

Quantity of milk in the final mixture E = 16 + 14 = 30 litres

Quantity of milk in the remaining mixture F = 15/31 x 93 = 45 litres

Quantity of milk in the final mixture F = 45 + 5 = 50 litres

Remaining mixture G = 136 – 34 = 102 litres

Quantity of milk in the remaining mixture G = 9/17 x 102 = 54 litres

Quantity of water in the remaining mixture G = 8/17 x 102 = 48 litres

Let the amount of milk added to remaining mixture G = y litres

(54 + y)/(48 + 2) = 6/5

=> (54 + y)/50 = 6/5

=> 5 x (54 + y) = 300

=> 270 + 5y = 300

=> 5y = 30

=> y = 6

Quantity of milk in the final mixture G = 54 + 6 = 60 litres

Required sum = 45 + 50 + 60 + 30 + 30 + 50 + 60 = 325 litres

5) Answer: b)

Remaining mixture G = 136 – 34 = 102 litres

Quantity of milk in the remaining mixture G = 9/17 x 102 = 54 litres

Quantity of water in the remaining mixture G = 8/17 x 102 = 48 litres

Let the amount of milk added to remaining mixture G = y litres

(54 + y)/(48 + 2) = 6/5

=> (54 + y)/50 = 6/5

=> 5 x (54 + y) = 300

=> 270 + 5y = 300

=> 5y = 30

=> y = 6

Quantity of milk in the final mixture G = 54 + 6 = 60 litres

Quantity of milk in mixture K = 60 x 125/100 = 75 litres

Quantity of water in the remaining mixture C = 3/8 x 72 = 27 litres

Quantity of water in the final mixture C = 27 + 3 = 30 litres

Quantity of water in mixture K = 30 x 90/100 = 27 litres

Total quantity of mixture K = 75 + 27 = 102 litres

Milk: water = 75:27 = 25:9

Remaining quantity of mixture K = 102 – 34 = 68 litres

Quantity of milk in the remaining mixture K = 25/34 x 68 = 50 litres

Quantity of water in the remaining mixture K = 9/34 x 68 = 18 litres

Quantity of milk in the final mixture K = 50 + 10 = 60 litres

Quantity of water in the final mixture K = 18 + 12 = 30 litres

Required difference = 60 – 30 = 30 litres