BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 1

Total Questions: 60

21. X and Y two alloys are made by mixing aluminum and magnesium metals in the ratio of 8: 5 and 9:16 respectively. If equal amounts of alloys are melted to form a new alloy Z, what will be the ratio of aluminum and magnesium in Z?

Correct Answer: (a) 317:333 
Solution:The ratio of aluminum and magnesium in Z
= [8/13 + 9/25] : [5/13 + 16/25] = 317/325 : 333/325 = 317:333

22. In a glass of syrup, water and sugar are mixed in the ratio 3: 2. If 8 liters of the mixture is replaced by 12 liters of sugar liquid, then the ratio of water and sugar becomes 1: 2. How many liters of water was in the glass?

Correct Answer: (b) 13.8 
Solution:

According to the first condition, Suppose, water and sugar are 3x liter and 2x liter respectively.
Remaining total mixture after removal of 8 liter
= (5x − 8) liter

The amount of water in this mixture = (5x − 8) × 3/5
= ((15x − 24)/5) liter

And quantity of sugar = (5x − 8) × 2/5

Quantity of sugar after adding 12 liter sugar = (5x − 8) × 2/5 + 12
= ((10x − 16)/5 + 12)
= (10x − 16 + 60)/5
= (10x + 44)/5

According to second condition
((15x − 24)/5) : (10x + 44)/5 = 1/2
⇒ 2(15x − 24) = (10x + 44)
30x − 48 = 10x + 44
44 + 48 = 30x − 10x
92 = 20x
x = 4.6

So, Amount of water = 3x = 3 × 4.6 = 13.8 liter

23. How many kilograms of sugar of Rs.5.4 per kg should be mixed with 10 kg of sugar of Rs.4.5 per kg, such that there may be gain of 20% by selling the mixture at Rs.5.94 per kg

Correct Answer: (a) 10 kg 
Solution:

Let, the amount of rice of Rs.5.4 per kg = x kg
According to the question,
x × 5.4 + 4.5 × 10 = 5.94 × (10 + x) ÷ 120 × 100

5.4x + 45 = 4.95 × (10 + x)
5.4x + 45 = 49.5 + 4.95x
5.4x − 4.95x = 49.5 − 45
0.45x = 4.5
x = 10 kg

24. A and B pulses of different quality, priced at Rs 70 per kg and Rs. 130 per kg respectively, are mixed. The new average price of the mixture obtained is Rs. 100 per kg. What is the ratio of the quantity of A and B in the mixture?

Correct Answer: (c) 1:1 
Solution:

According to Question –

A        B
70      130

        100

130 − 100 = 30   100 − 70 = 30

(Quantity of A / Quantity of B) = 30/30
Ratio = 1:1

25. Silver is 34 times heavier than water and brass is 18 times heavier than water. In what ratio should both the metals be mixed so that they become 24 times heavier than water?

Correct Answer: (c) 3:5 
Solution:

According to Question –

Silver      Brass
34        18

        24

6        10

That is, both metals have to be mixed in the ratio 3:5.

26. In what proportion should rice costing Rs. 20 per kg be mixed with another variety of rice costing Rs. 15 per kg so that the mixed rice obtained has a profit of 20% by selling it at the rate of Rs. 20.40 per kg?

Correct Answer: (b) 2:3 
Solution:

Sale price of new rice = 20.40 Rupees per kg, and profit = 20%
Hence the purchase price per kg of new rice
= Sale price / (100 + profit %) × 100
= 20.4/(100 + 20) × 100 = 20.4/120 × 100
= 17 Rupees per kg

Now by Alligation method –

First type of rice    Second type of rice
20            15

        17

2            3

Intended ratio = 2:3

27. In a milk water mixture 2/3 part is milk. The total volume of the mixture is 42 liters. If 8 liters of water is added to it, what will be the percentage of milk in the mixture?

Correct Answer: (b) 56 
Solution:

Amount of milk in the mixture = 2/3 × 42 liters
And the amount of milk = 28 liters

According to Question,
The total mixture after mixing the amount of water
= 42 + 8 = 50 liters

Percent of milk = quantity of milk / volume of total mixture × 100 liters
Percent of milk = 28/50 × 100 liters
Milk percentage = 56%

28. The ratio of Alcohol and water in two pots is 2 : 5 and 4 : 3, find the ratio of alcohol and water in the new mixture obtained (in the third new vessel) after mixing the mixture of the two pots.

Correct Answer: (c) 3 : 4 
Solution:

Intended ratio = (2/7 + 4/7) : (5/7 + 3/7)
= 6/7 : 8/7
= 6 : 8
= 3 : 4

29. A mixture of 10 liters of sugar contains 11% sugar, out of which 2 liters of water becomes steam. Find the percentage of sugar in the remaining mixture.

Correct Answer: (b) 13.75% 
Solution:

Sugar content (10 × 11)/100 = 1.1
Remaining mixture = 8 liters

The percentage of sugar in the remaining mixture
= (1.1/8) × 100 = 13.75%

30. In what ratio should 30% milk solution be mixed with 60% milk solution so that the resulting solution contains 40% milk?

Correct Answer: (c) 2 : 1 
Solution:

According to Question –

P₁        P₂
30        60

        40

20        10

Intended ratio = 20 : 10 = 2 : 1