FOR FREE YEAR SOLVED

1. Two alloys are the both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5, in what ratio should the alloys be mixed to obtain a new alloy in which the ratio of tin and copper is 8 : 3?

(a) 3 : 5                                                                   

(b) 4 : 7

(c) 3 : 8                                                                    

(d) 5 : 11

Answer: 

First Alloy 

Copper : Tin = 1 : 3

Second Alloy 

Copper : Tin = 2 : 5

New Alloy 

Copper : Tin = 3 : 8

Considering Copper

L.C.M of (denominators) 4, 11, 7 = (4 x 11 x 7)

[Dividing the LCM by the denominators and multiplying the factor with the numerator]

1st Alloy : 2nd Alloy 

= 4 : 7

(b) is the correct option.

2. A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is:

(a) 3 liters                                           

(b) 4 liters

(c) 15 liters                                         

(d) 10 liters

Answer: 

On adding 5 liters of water it raised from 3 units to 5 units that means

(d) is the correct option.

3. In the alloys a and B, the ratio of Zinc to tin is 5 : 2 and 3 : 4 respectively. Seven kg of the alloys A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of zinc and tin in the new alloy?

(a) 2 : 1                                                                   

(b) 1 : 2

(c) 2 : 3                                                                    

(d) 1 : 1

Answer: 

Zinc and Tin ratio in -

Alloy A (7kg)     Alloy B (21 kg)

      5 : 2                      9 : 12

After Mixing,

5 + 9 :  2 + 12

= 14 : 14

= 1 : 1

(d) is the correct option.

4. Zinc and copper are in the ratio 5 : 3 in 400 gm of an alloy. How much copper (in grams) should be added to make the ratio 5 : 4?

(a) 50                                                                     

(b) 66

(c) 72                                                                     

(d) 200

Answer:

Copper composition increases from 3 units to 4 units, i.e. 1 unit

From the question, Zinc (5 unit) + Copper (3 units) = 8 units = 400gm

That means,

(a) is the correct option.

5. 15 liter of a mixture contains alcohol and water in the ratio 1 : 4. If 3 liters of water is mixed in it the percentage of alcohol in the new mixture will be:

Answer:

In 15 liters of mixture,

(b) is the correct option.

6. A and B are two alloys of gold and copper in the ratio 7 : 2 and 7 : 11 respectively. If equal quantities of these two alloys are melted to form a new alloy C, then the ratio of gold and copper in C is:

(a) 6 : 5                                                                 

(b) 9 : 4

(c) 12 : 7                                                                               

(d) 7 : 5

Answer:

If (A) is multiplied by 2 then the new weight will be the same as that of B, i.e. 18 units.

Alloy C = 2A + B

(d) is the correct option.

7. The milk and water in two vessels A and B are in the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?

Answer: 

Considering Milk,

Taking LCM of the (denominators) 7, 5, 2 as (7 x 5 x 2) and equalizing the denominators followed by modifying the numerators.

(b) is the correct option.

8. A vessel contains a mixture of milk and water in the respective ratio of 3 : 1.32 litres of the mixture was taken out and replaced with the same quality of milk so that the resultant ratio between the quantities of milk and water in the mixture was 4:1 respectively. If 10 litres of mixture is again taken out from the vessel, what is the resultant quantity of water in the mixture ( in litres)? 

(a) 24

(b) 30

(c) 20

(d) 26

(e) 32                                                                                         

Answer:      

Milk : Water

Initially,       

3 : 1

After 32 litre of the mixture is taken out, the ratio remains the same.

3 units of milk are raised to 4 units after 32l of milk is added.

So, 

After 10l of the mixture is taken out, then the quantity of water taken out is 

So, option b is the correct answer.

9.  A vessel contains a mixture of Grape, Pineapple, and Banana juice in the respective ratio of 4 : 6 : 5 : 15 litres of this mixture is taken out and 8 litres of grape juice and 2 litres of pineapple juice is added to the vessel. If the resultant quantity of Grape juice is 10 litres less than the resultant quantity of pineapple juice, what was the initial quantity of mixture in the vessel ( in litres)? 

(a) 120

(b) 150

(c) 105

(d) 135

(e) 90

Answer:

After taking out 15l of the mixture the ratio remains the same. 

According to the problem, 

(6x + 2) – (4x + 8) = 10

⇒ 2x – 6 = 10 ⇒ x ⇒ 8

So, after taking out 15l, the quantity of the mixture was 4x + 6x + 5x = 15x = 15  8 = 120l.

Initial Quantity of the mixture = 120l + 15l = 135l 

So, the correct option is d.

10. In a 90 litres mixture of milk and water, the percentage of water is only 30 %. The milkman gave 18 litres of this mixture to a customer and then added 18 litres of water to the remaining mixture, what is the percentage of milk in the final mixture? 

(a) 64

(b) 48

(c) 52

(d) 68

(e) 56

Answer:

In 90l mixture, 

After giving an 18l mixture to a customer, the ratio in (90 – 18) = 72l mixture remains the same.

So, the correct option is e.

11. A 20-litre mixture contains milk and water in the respective ratio of 3 : 2. 10 litres of the mixture is removed and replaces with pure milk and the operation is repeated once more. At the end of the two removals and replacement, what is the ratio of milk and water in the final mixture? 

(a) 17 : 3

(b) 9 : 1

(c) 4 : 17

(d) 5 : 3

(e) 3 : 14

Answer:

Initially, M : W = 3 : 2

Total quantity of mixture = 20l 

Quantity Ratio, 

10l of the mixture is taken out (milk = 6l, water =4l) 

Let Quantity Ratio, 

10l of milk is added, 

Again, 10l of mixture (M = 8l, W = 2l) is taken out, 

Again, 10l of milk is added, 

Final ratio of M and w = 9 : 1 

So, the correct option is b.

12. 18 litre of pure water was added to a vessel containing 80 litre of pure milk 49 litre of the resultant mixture was then sol and some more quantity of pure milk and pure water was added to the vessel in the respective ratio 2 : 1. If the resultant ratio of milk and water in the vessel was 4 : 1, what was the quantity of pure milk added to the vessel? (in litres) 

(a) 4

(b) 8

(c) 10

(d) 12

(e) 2

Answer:

49l of the mixture is taken out and then means 40l of milk and 9l of water is taken out.

Remaining Quantity ratio, 

80l – 40l : 18l – 9 Some quantity of a mixture of 2 : 1 ratio is added.

40l + 2x : 9l + x 

[Where 2x and x are the quantities of the 2  and mixture ]according to the problem, 

So, the correct option is a. 

13. Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filed to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in the vessel? 

(a) 1 : 3

(b) 2 : 3

(c) 3 : 2

(d) 5 : 3

Answer:

According to Allegation on milk

So, the correct option is d.

14. The monthly average salary paid to all the employees was Rs. 5000. The monthly average salary paid to male and female employees was Rs. 5200 and Rs. 4200 respectively. Then the percentage of males employed in the company is: 

(a) 75 % 

(b) 80 % 

(c) 85 % 

(d) 90 % 

Answer:  

Applying allegation trick,

So, the correct option is (b).