BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 1

Total Questions: 60

31. The mixture of alcohol and water in two pots, P and Q, is in the ratio 4 : 5 and 3 : 2. In what proportion can these two mixtures be mixed to obtain a new mixture of half alcohol and half water?

Correct Answer: (b) 9 : 5 
Solution:

According to Question -
P(Alcohol)  Q(Alcohol)
4/9      3/5

        1/2

1/10     1/18

Intended ratio = (1/10) : (1/18) = 9:5

32. The 30 liter beer contains 5% alcohol. How many liters of water should be added to the beer so that the alcohol content becomes 3%?

Correct Answer: (a) 20 liter 
Solution:

Alcohol content in 30 liters of beer = 30 × (5/100)
= (3/2) = 1.5 liter

Suppose the amount of water added = x liter
By question,
(30 + x) × 3/100 = 1.5
30 + x = 50 ⇒ x = 20 liter

33. A drum of beer has water and alcohol in the ratio 7:5. If 9 liters of the mixture is replaced by 10 liters of alcohol, then the ratio of water and alcohol becomes 7:9. How many liters of water was in the drum?

Correct Answer: (b) 22.75 
Solution:

Suppose water and alcohol in a drum is 7x and 5x respectively.
Remaining total mixture after removing 9 liters =
(12x − 9) liters

Quantity of water in this mixture = (12x − 9) × 7/12
= (28x − 21)/4 liter

And the amount of alcohol = (12x − 9) × 5/12

The amount of alcohol in the mixture again on filling
10 liters of alcohol
= (12x − 9) × 5/12 + 10
= (60x − 45)/12 + 10
= (60x − 45 + 120)/12
= (60x + 75)/12
= (20x + 25)/4

According to second condition
∴ (28x − 21)/4 × 4/(20x + 25) = 7/9
⇒ 7(20x + 25) = 9(28x − 21)
140x + 175 = 252x − 189
175 + 189 = 252x − 140x
364 = 112x
(x = 3.25)

(Water = 7x = 7 × 3.25 = 22.75) Liter

34. A pot of honey extracted from the jungles of Kolkata contains 40% carbohydrates. Part of it is replaced by other honey, which has 19% carbohydrate, then the new mixture has 26% carbohydrate. How much honey was replaced?

Correct Answer: (a) 2/3
Solution:

carbohydrates  carbohydrates
40%       19%

        26%

7        14
1        2

Honey content = 2/3

35. At the Heineken Beer Company four drums of similar size are filled with beer. The alcohol content in the four drums is 80%, 75%, 60% and 50% respectively. If all four drums are mixed, what will be the ratio of water and alcohol in the mixture obtained?

Correct Answer: (b) 27 : 53 
Solution:

I II III IV
(A) Alcohol → 80 75 60 50
(W) Water → 20 25 40 50

A:W  A:W  A:W  A:W

I = 80:20 II = 75:25 III = 60:40 IV = 50:50
= 4:1   = 3:1   = 3:2   = 1:1

According to Question,
A:W = (4/5 + 3/4 + 3/5 + 1/2) : (1/5 + 1/4 + 2/5 + 1/2)
A:W = ((16 + 15 + 12 + 10)/20) : ((5 + 4 + 8 + 10)/20)
= 53 : 27
Or, W : A = 27 : 53

36. From a drum containing 50 liters of pure honey from Patanjali, 10 liters of honey are extracted and 10 liters of preservatives are added. If this process is repeated three times, what is the ratio between ultimately preservative and honey?

Correct Answer: (c) 61 : 64 
Solution:

Amount of pure honey in the drum
= 50(1 − (10/50))³
= 50(1 − (1/5))³
= 50 × (4/5) × (4/5) × (4/5) = 128/5 Liter

Quantity of preservatives = 50 − 128/5
= (250 − 128)/5 = 122/5

Preservative : Honey = 122/5 : 128/5 = 61 : 64

37. How many liters of preservatives should be added to a 16 liter cough syrup with 10% preservatives, so that the amount of preservatives in the mixture is 20%?

Correct Answer: (a) 2 liters 
Solution:

Let x liters preservative be added
The amount of syrup in the beginning = The quantity of syrup in the end

16 × 90 = (16 + x) × 80
144 = 128 + 8x
144 − 128 = 8x
16 = 8x
x = 2 Liter

38. The initial ratio of maida and flour in saltpeter was 17:28. How much flour is added to the raw material of 27 kg saltpeter so that ratio of maida and flour becomes 2:5?

Correct Answer: (b) 8.7 kg 
Solution:

Total quantity of raw material = 27 Kg
Maida and Flour Ratio = 17:28

∴ Quantity of maida =
(17×27)/(17+28) = (17×27)/45 = 51/5 kg

∴ Quantity of flour =
(28×27)/(17+28) = (28×27)/45 = 84/5 kg

Suppose if (x) kg of flour is added to it,

(51/5) / (84/5 + x) = 2/5
⇒ 5(51/5) = 2(84/5 + x)
⇒ 51 = (168/5 + 2x)
⇒ 255 = 168 + 10x
⇒ 10x = 255 − 168 = 87
Or, x = 8.7 kg

39. Three varieties of almonds Rs.25200 per quintal, Rs.28000 per quintal and Rs.31600 per quintal is sold. What will be the profit or loss on selling 274 kg of the first variety, 197 kg of the second variety and 54 kg of the third variety at the rate of Rs.28350 per quintal?

Correct Answer: (a) Profit of Rs.7565.50
Solution:

Total price of all three types of almonds
= 252×274 + 280×197 + 316×54
= 69048 + 55160 + 17064 = Rs.141272

Total value of mixture = (274 + 197 + 54) × 283.50
= 525 × 283.50 = Rs.148837.5

Thus, the total profit on sales = 148837.5 − 141272
= Rs.7565.50

40. Preservatives of Rs. 225 per kg and Rs. 275 per kg are used to protect syrup. In what proportion should both preservatives be mixed so that the mixture obtained becomes Rs. 253.4 per kg (approx).

Correct Answer: (d) 3 : 4 
Solution:

According to Question

Cheap    costly
225     275

      253.4

21.6    28.4

Cheap : Costly = 21.6 : 28.4
= 216/284 = 54/71
≈ 54/72 = 3/4

Cheap : costly = 3 : 4