BANK & INSURANCE (MIXTURE AND ALLIGATION) PART 2

Total Questions: 60

11. Trader buys two types of rice at Rs. 80/kg and Rs. 60/kg and mixes these two in a ratio A : B, respectively, such that when he marks the price as Rs. 100/kg, he makes 20% profit even after giving 22% discount. Find A : B

Correct Answer: (c) 1 : 3
Solution:

Marked price = 100
⇒ SP = 100 − 22 = 78
⇒ CP = (78 × 100) / (100 + 20) = 65

Using Alligation method
⇒ A : B = (65 − 60) / (80 − 65)
⇒ A : B = 1 : 3

12. A and B are two alloys of gold and copper prepared by mixing metals in the ratios 5 : 3 and 5 : 11 respectively. Equal quantities of these alloys are melted to form a third alloy C. The ratio of gold and copper in the alloy C is

Correct Answer: (e) None of these
Solution:

Gold in 1 kg of A = 5/8
Copper in 1 kg of A = 3/8
Gold in 1 kg of B = 5/16
Copper in kg of B = 11/16

Gold in 2 kg of C = (5/8) + (5/16) = 15/16
Copper in 2 kg of C = (3/8) + (11/16)
⇒ 17/16

Ratio of gold to copper in C = (15/16) : (17/16)
⇒ 15 : 17

∴ Required ratio is 15 : 17

13. A jar contains a mixture of orange juice and water in the ratio of 4 : 1. An amount of 75 litres of the mixture was taken out and 25 litres of water was added to it. If the water was 40% in the resultant mixture, what was the initial quantity of the mixture in the jar?

Correct Answer: (b) 150 litres 
Solution:

Let the quantity of orange juice and water be 4x and x respectively.
Total quantity = 5x

Quantity of orange juice drawn when 75 litres mixture was withdrawn
= 4/5 × 75 = 60

Quantity of water drawn when 75 litres mixture withdrawn
= 1/5 × 75 = 15

Quantity of orange juice remain in the mixture when 75 litres mixture was withdrawn = 4x − 60

Quantity of water remained in the mixture when 75 litres mixture was withdrawn and 25 litres of water was added to it = x − 15 + 25 = x + 10

According to the question,
(x + 10)/(4x − 60) = {40% / (100 − 40)%} = 40% / 60% = 40/60

6x + 60 = 16x − 240
10x = 300
∴ x = 30

Initial quantity of the mixture = 4x + x = 5x
Initial quantity of the mixture = 5 × 30 = 150 litres

14. In a 64 liter of mixture of milk and water, the quantity of water is 20 liter and the rest is milk. 1/4th of the mixture is taken out. How much milk should be added in the mixture so that the quantity of milk would be 3 times the quantity of water?

Correct Answer: (e) None of these
Solution:

1/4 th of the mixture is taken out
Means quantity of milk has taken out
⇒ 1/4 th of 44 = 11 liter

And the quantity of water has taken out
⇒ 1/4 th of 20 = 5 liter

Remaining Quantities of milk and water is 33 liter of milk and 15 liters of water

Now we have to make it in the ratio of 3 : 1 by adding milk

(33 + x) / 15 = 3/1
⇒ x = 12 liter

15. The total selling price of a mixture of colours prepared from red and purple colours is Rs. __. If the seller has 300 gms of red colour costing Rs. 450 per kg and 75 gms of purple colour costing Rs. 3.33 and he has planned to mix them in the ratio 3 : 1. He also has planned to use the entire purple colour in the mixture and maximum part of red colour in the mixture while maintaining the planned ratio.

Correct Answer: (e) None of these
Solution:

By taking the values from equation 1,
The seller can mix the red and purple colours either in the ratio 3 : 1 or 1 : 3. But as he has planned to sell all the purple colour and maximum of red colour, he will mix the red colour and purple colour in the ratio 3 : 1

If the seller mixed red and purple in the ratio 3 : 1
Amount of purple colour used = 75 g (as he has to use all of it)
∴ Amount of red colour used = 3 × 75 g = 225 g

If we consider the ratio 1 : 3 for red and purple colours, then:
Amount of purple colour used = 75 g (as he has to use all of it)
Amount of red colour used = 1/3 × 75 = 25 g

But, the seller had to use it maximum.
The upper condition is more exact.

Now,
Cost of 75gms of purple colour = Rs. 3.33
Cost of 225g of red colour = 450/1000 × 225 = Rs. 101.25

Total mass of mixture = 75g + 225gm = 300gm
∴ Total cost of mixture = Rs. (101.25 + 3.33)
= Rs. 104.58

16. A milk vendor has 2 buckets of milk. In which the first is containing 25% of water rest milk while the second is containing equal proportion of milk & water. How much mixture should be removed from each bucket so that mixture contains 12 litres in ratio 3 : 5 (water : milk)?

Correct Answer: (b) 6 litre 
Solution:

In First bucket, milk = 75%/100% = 3/4
In Second bucket, milk = 1/2

In mixture, milk = 5/8

Ratio of two mixtures,
Using allegation,

(Bucket 1)  (Bucket 2)
1/4      1/2

    5/8 (Final mixture)

 1/8      1/8

So, quantity of mixture to be taken from each mixture
= 1/2 × 12 = 6 litres

17. In a 64 litre mixture of milk and water, the ratio of milk and water is 15 : 1. When 24 litre of mixture is removed and 5 litre of milk and water each is added, then find the difference between the quantity of milk and water in the final mixture

Correct Answer: (e) 35 litre
Solution:

Given
The ratio of milk and water is 15 : 1

Let quantity of milk be 15x and water be x

Now
15x + x = 64 ⇒ 16x = 64
⇒ x = 4

∴ Quantity of milk in initial mixture = 15x = 15 × 4
= 60 litre

And quantity of water in initial mixture = x = 4 litre

24 litre of mixture is removed
∴ The total new mixture = 64 − 24 = 40 litre

Again
The ratio of milk and water is 15 : 1

Let quantity of milk be 15x and water be x

Now
15x + x = 40
⇒ 16x = 40
⇒ x = 5/2

∴ Quantity of milk in new mixture = 15x = 15 × 5/2
= 37.5 litre

And quantity of water in new mixture = x = 2.5 litre

After adding 5 litre milk total quantity of milk = 37.5 + 5 = 42.5 litre
Also After adding 5 litre water total quantity of water = 2.5 + 5 = 7.5 litre
The difference between the quantity of milk and water in the final mixture = 42.5 − 7.5 = 35 litre

18. A jar contains only 12 liters of milk and the rest is water. A new mixture in which the concentration of milk is 30%, is to be formed by replacing the jar mixture. How many liters of the mixture shall be replaced with pure milk if initially there were 48 liters of water in the mixture?

Correct Answer: (e) 7.5 litres
Solution:

Milk : water
12 : 48
Ratio = 1 : 4
Initial mixture = 12 + 48 = 60 litres

Using the Alligation method
Milk  Puremilk
20%  100%

  30%

70%  10%
7    1

Remaining : Replaced
Initial Mixture = 8 unit

8 units = 60 liters
1 unit = 7.5 litre

7.5 liters of mixture of water and milk is replaced with pure milk

19. Two identical jars H and W of capacity 70 litres each containing 30 litres of pure alcohol and 30 litres of pure water respectively. 6 litres of alcohol is taken from H and poured into W and then 12 litres of mixture from W is taken and poured into H. What is the ratio of alcohol in H and W?

Correct Answer: (d) 13 : 2 
Solution:

Jar H contains 30 litre pure alcohol.
Jar W contains 30 litre pure water.
6 litres of alcohol is taken from H and poured into W.
Now, jar H contains 24 litre pure alcohol.
Jar W contains 30 litre water & 6 litre alcohol.
∴ Ratio of water & alcohol = 5 : 1

Again, 12 litres of mixture from W is taken and poured into H.
∴ In this 12 litre mixture, amount of water = 10 litres & alcohol = 2 litres.
∴ After addition, amount of alcohol in H = (24 + 2) = 26 litres.
After removal, amount of alcohol in W = (6 − 2) = 4 litres.

The ratio of alcohol in H & W = 26 : 4 = 13 : 2

20. 270 litres of a mixture contains wine and water in the ratio of 5 : x. After addition of 20 litres of water and 30 litres of wine to it, the ratio of wine to water in the resultant mixture becomes 9 : 7. Find the value of x.

Correct Answer: (d) 4 
Solution:

The quantity of wine in initial mixture = 5/(5+x) × 270
= 1350/(5+x)

Quantity of water in initial mixture = 270x/(5+x)

Using the data provided in the question, we get:

(1350/(5+x) + 30) / (270x/(5+x) + 20) = 9/7

1500 + 30x
────────── = 9/7
270x + 100

1500 × 7 + 210x = 900 + 2610x
= 10500 − 900 = 2400x
∴ x = 4