BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 1

Total Questions: 60

41. In what proportion should buffalo milk costing Rs. 40 per kg be mixed with cow’s milk at Rs. 30 per kg so that there is a profit of 20% on selling the mixture at the rate of Rs. 40.8 per kg.

Correct Answer: (b) 2 : 3 
Solution:

Sale price of the mixture = Rs. 40.8 per kg and profit = 20%
Hence the cost price per kg of the mixture
= selling price / (100 + profit %) × 100
= 40.8/(100 + 20) × 100 = 40.8/120 × 100
= 34 rupees per kg

Now By alligation method-

Buffalo milk   cow’s milk
40         30

        34

34 − 30 = 4
40 − 34 = 6

= 2      = 3

Intended ratio = 2 : 3

42. In what ratio should Rs. 50 per kg and Rs. 60 per kg of sugar be mixed so that 20% profit is made by selling the mixture at Rs. 70 per kg?

Correct Answer: (c) 1 : 5 
Solution:

According to Question

I      II
50     60

      175/3

60 − 175/3 = 5/3
175/3 − 50 = 25/3

I : II = 1 : 5

43. Two types of tea, priced at Rs.380 per kg and Rs.420 per kg, are mixed in the same quantity. And are sold at a rate of Rs.450 per kg. Find the percentage profit.

Correct Answer: (b) 12.5% 
Solution:

Price of first type of tea = Rs.380/kg
Price of second type of tea = 420/kg
Cost price of both types of tea = (380 + 420)
= Rs.800

Sale price of both types of tea = 450 × 2 = Rs.900

Profit = selling price - Cost price
= 900 − 800 = 100

Profit % = profit/cost price × 100
= 100/800 × 100 = 12.5%

44. What is the amount of egg in a 1 kg cake, if the cake contains 32% egg, 40% flour and the rest sugar?

Correct Answer: (d) 320 gm 
Solution:

Cake = 1 kg = 1000
Total cake = 100%

100

32%   40%   28%
Egg   Flour  Sugar

Egg content = 1000 × 32/100 = 320 gm

45. Cow and buffalo milk, which are priced at Rs.25 and Rs.35 per kg respectively, mixed in ratio of 4:6 and selling at the rate of Rs.37 per kg, the profit percentage will be approximately?

Correct Answer: (a) 20% 
Solution:

Cost price of cow’s milk = 25 × 4 = 100
Cost price of buffalo’s milk = 35 × 6 = 210
Total purchase price = Rs.310

Total selling price = 37 × 10 = Rs.370

In question -
selling price = (Cost price (100 + P%))/100
⇒ 370 = (310 × (100 + P%))/100
37000 − 31000 = P% × 310
6000/31 = P%
P% = 19.35%
P% = 20% (Approx)

46. To get 25% profit on milk at the rate of Rs. 30 per kg, in what proportion will the milk of cow and buffalo have to be mixed, if there is a loss of 20% on selling cow’s milk at Rs.16 per kg and Rs. 40 per kilogram of buffalo milk has a profit of 20%?

Correct Answer: (c) 2:1 
Solution:

Suppose cow’s milk is x part and buffalo milk is y part.
According to Question,
(16x + 40y)/(x + y) × 125/100 = 30
(16x + 40y)/(x + y) × 5/4 = 30
16x + 40y = 24 (x + y)
(24 − 16)x = (40 − 24)y
8x = 16y
x = 2y
x/y = 2/1
xy = 2:1

47. The ratio of water and alcohol in one drum of wine is 4:3 and in the other drum the ratio is 3:2. What will be the ratio of water and alcohol when both are mixed in the ratio of 1:2 respectively?

Correct Answer: (b) 62:43 
Solution:

Volume of water in first drum = 4/7
And the quantity of alcohol = 3/7

Volume of water in second drum = 3/5
And the amount of alcohol = 2/5

According to the question, by mixing the two mixtures in the ratio 1:2

= (4/7 × 1 + 3/5 × 2) / (3/7 × 1 + 2/5 × 2)
= (4/7 + 6/5) / (3/7 + 4/5)
= (20 + 42)/(15 + 28) = 62/43

Desired ratio = 62:43

48. In what ratio should Rs. 35 per kg of cow's milk and Rs. 65 per kg of buffalo milk be mixed so that the new price of the mixture becomes Rs. 50 per kg?

Correct Answer: (c) 1:1 
Solution:

According to Question -

35     65

     50

65 − 50 = 15
50 − 35 = 15

Cow’s milk / buffalo milk = 15/15
Ratio = 1 : 1

49. In what proportion should the two liquor drums, where alcohol and water are in the ratio of 3:1 and 5:3 respectively, be mixed so that in mixture ratio of alcohol and water is 2:1?

Correct Answer: (a) 1:2 
Solution:

Alcohol in the first drum = 3/(1 + 3) = 3/4
Alcohol in second drum = 5/(3 + 5) = 5/8
Alcohol in new mixture = 2/(1 + 2) = 2/3

(1)     (2)
3/4     5/8

      2/3

(2/3 − 5/8) : (3/4 − 2/3)
= 1/24 : 1/12 = (1 : 2)

50. The two drums of Roohafza have sugar and water in the ratio of 5: 3 and 7: 9 respectively. What will be the new ratio of sugar and water when these two drums are mixed?

Correct Answer: (a) 17:15 
Solution:New ratio of sugar and water
= [5/8 + 7/16] : [3/8 + 9/16]
= 17/16 : 15/16 = 17 : 15