BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 2

Total Questions: 60

1. Vessel A contains (2x + 360) liters mixture of milk and water in the ratio of 7:5 and vessel B contains a 200 liters mixture of milk and water in the ratio of 3:2. If vessels A and B are mixed together, then the ratio of the milk and water becomes 47:33. Find the value of x.

Correct Answer: (c) 120 
Solution:

Milk in vessel B = 3/5 × 200 = 120
Water in vessel B = 2/5 × 200 = 80

(7y + 120)/(5y + 80) = 47/33
235y + 3760 = 231y + 3960
y = 50

2x + 360 = 12 × 50
x = 120

2. Two types of oil, A and B have been mixed in the ratio of 3:2 and total mixture is 90 liters. When one third of mixture was consumed, some more quantity of oil A was mixed with the mixture and the ratio was made 2:1. The quantity of oil A mixed later on was:

Correct Answer: (d) 12 L 
Solution:

Quantity of type A oil in the mixture = 3/5 × 90
= 54 L

Quantity of type B oil in the mixture = 2/5 × 90
= 36 L

After consuming one third mixture:

Quantity of type A oil = 2/3 × 54 = 36 L
Quantity of type B oil = 2/3 × 36 = 24 L

Let x litres of type A oil is mixed with the mixture, then
(36 + x)/24 = 2/1
⇒ 36 + x = 48
⇒ x = 48 − 36
⇒ x = 12

∴ 12 L of type A oil was mixed with the mixture later on.

3. A is 120 liter of mixture of milk and water in the ratio 17 : 7. 40% of mixture is poured out and poured into vessel X. Vessel X contain a 100 liter mixture of equal milk and water. Find the new ratio of milk and water.

Correct Answer: (b) 21 : 16 
Solution:

Quantity of milk and water in 120 liter of mixture:
Mixture of milk = 17/24 × 120 = 85 liter
Mixture of water = 120 − 85 = 35 liter

Now, according to question
Quantity of mixture taken out and poured in vessel X:
Mixture of milk poured out = 85 × 2/5 = 34 liter
Mixture of water poured out = 35 × 2/5
= 14 liter

Again, from the question
X is a 100 liter mixture of equal milk and water means
50% milk and 50% water

Then,
New ratio of milk and water after addition
= (50 + 34) : (50 + 14)
= 84 : 64
⇒ 21 : 16

∴ New ratio of milk and water is 21 : 16

4. The milk and water in two vessels A and B are in the ratio of 7 : 9 and 6 : 5 respectively. In what ratio the liquids are mixed to obtain a new mixture vessel C containing half milk and half water?

Correct Answer: (a) 8 : 11 
Solution:

Milk and water in two vessels A and B are in the ratio of 7 : 9 and 6 : 5 respectively.
Now, let us take the ratio of either milk or water from vessel 1 and vessel 2.

Amount of milk in vessel A = 7x/(7+9) = 7x/16
Amount of milk in vessel B = 6y/(6+5) = 6y/11

Amount of water in vessel A = 9x/16
Amount of water in vessel B = 5y/11

On equating the sum of the amount of milk equal to the sum of the amount of water we get,
7x/16 + 6y/11 = 9x/16 + 5y/11
⇒ x/y = 8/11

5. Kiran sells two types of milk. In the first type of milk, there is 40% milk is present and the rest is water, whereas, in the second types only 40% water is present. He takes 30 litres and 20 litres of mixture from both types respectively. What is the percentage of milk present in the new mixture?

Correct Answer: (c) 48%
Solution:

Milk present in 30 litres of mixture = 30 × (40/100) litres = 12 litres

Milk present in 20 litres of mixture = 20 × {(100 − 40)/100} litres = 12 litres

After mixing the two types of milk, the total mixture
= (30 + 20) litres = 50 litres

So, pure milk in the new mixture = (12 + 12) litres = 24 litres

So, the percentage of milk present in new mixture = (24/50) × 100 = 48%

∴ The percentage of milk present in the new mixture is 48%

6. In a grocery shop box A contains wheat worth Rs. 30 per kg and box B contains wheat worth Rs. 40 per kg. If both box A and B are mixed in the ratio 4 : 7 then the price of mixture per kg is approximately:

Correct Answer: (b) Rs. 36 
Solution:

CP of 1 kg of cheaper quantity (c)
Rs.30

CP of 1 kg of Dearer quantity (d)
Rs.40

Mean Price (m)
Rs.X

(d − m) = (40 − x)  (m − c) = (x − 30)

So, (Cheaper quantity) : (Dearer quantity) = (d − m) : (m − c)
= (40 − X) : (X − 30)

According to question,
Given ratio = 4/7

So, 4/7 = (40 − X)/(X − 30)
⇒ 280 − 7x = 4x − 120
⇒ 11x = 400
⇒ x = 36.36 ≈ 36

∴ The price of mixture of 1 kg wheat is approximately Rs. 36

7. A container contains 96 litres mixture of milk and water with 35% milk If 16 litres of the mixture is taken out and then 10 litres of water is added. What is the ratio of milk and water in the new mixture?

Correct Answer: (d) 14 : 31 
Solution:

A container contains mixture of milk and water = 96 liters

If 16 liters of mixture is taken out, then remaining quantity of mixture = 96 − 16 = 80 L

Quantity of milk in the remaining mixture
= 80 × (35/100) = 28 L

Quantity of water in the remaining mixture = 80 − 28 = 52 L

If 10 liters water added, then quantity of water
= 52 + 10 = 62 Liters

Ratio of milk and water in the new mixture = 28 : 62
= 14 : 31

8. A container contains 63 litres of mixture of milk and water. The respective ratio of milk and water is 5 : 4. From the container 18 litres of mixture was extracted and 5 litres of pure milk was added. What is the percentage of water?

Correct Answer: (c) 40%
Solution:

Mixture = 5x + 4x
⇒ 9x = 63
⇒ x = 7

Milk = 5 × 7
⇒ 35 liters

Water = 4 × 7
⇒ 28 liters

18 liter of mixture taken out,
Milk = 35 − 18 × (5/9)
⇒ 35 − 10
⇒ 25

Water = 28 − 18 × (4/9)
⇒ 28 − 8
⇒ 20

5 liter pure milk was added,
Milk = 25 + 5
⇒ 30

Total mixture = 30 + 20
⇒ 50

Percentage of water,
⇒ (20/50) × 100
⇒ 40%

∴ The percentage of water is 40%

9. There is a 56 L solution having milk and water in the ratio of 5:3 respectively. 8 L of solution is removed and 2 L of milk and 6 L of water is added to remaining solution. What will be the final ratio of milk and water in the solution?

Correct Answer: (e) 4:3
Solution:

Let the ratio be x

Then the initial quantity of milk = 5x
And initial quantity of water = 3x

∴ Quantity of milk = 5x/8x × 56
⇒ 35 L

And quantity of water = (56 − 35) L = 21 L

Now, 8 L of solution is removed.
∴ Quantity of milk removed from solution = 5x/8x × 8 L
⇒ 5 L

And quantity of water removed = (8 − 5) L = 3 L

Now, 2 L of milk and 6 L of water is added.

∴ Final ratio = (35 − 5 + 2)/(21 − 3 + 6)
⇒ 32 : 24
⇒ 4 : 3

∴ The final ratio of milk and water is 4 : 3

10. Solution A has 3 : 4 milk to water ratio and solution B has 5 : 2 milk to water ratio. In what proportion solution A and B should be mixed respectively to obtain 1 : 1 milk to water ratio?

Correct Answer: (e) 3 : 1
Solution:

Milk in the mixture = 3x + 5y
Water in the mixture = 4x + 2y

∴ (3x + 5y)/(4x + 2y) = 1
⇒ 3x + 5y = 4x + 2y
⇒ x/y = 3

⇒ Ratio of A : B = 3 : 1