# CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement

**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

A milkman dilutes 36 litres of milk with water. The percentage of milk in the solution is now 80%. How many litres of water does he add?

- (a)
6

- (b)
9

- (c)
12

- (d)
18

Answer: Option B

**Explanation** :

Original milk contains 100% milk. Water contains 0% milk.

Resultant mixture contains 80% milk.

∴ Using Alligation, we are mixing a liquid with 100% milk with another liquid with 0% milk to give a liquid that has 80% milk.

∴ Ratio of Milk and Water = 80 : 20 = 4 : 1

∴ If there are 36 litres of milk

∴ 4 : 1 = 36 : x

∴ x = 9

Hence, option (b).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

How much chicory at Rs. 40 a kg should be added to 15 kg of tea at Rs. 100 a kg, so as to make the mixture worth Rs. 65 a kg?

- (a)
17 kgs

- (b)
21 kgs

- (c)
25 kgs

- (d)
22 kgs

Answer: Option B

**Explanation** :

∴ Required ratio of quantity of chicory and tea = 7 : 5

∴ Amount of Chocory / Amount of Tea = 7 / 5

∴ Amount of Chicory = 7/5 × 15 = 21 kg

Hence, option (b).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

Aakash invested some part of Rs 5,00,000/- in stock X and the remaining part in stock Y. At the end of the year, Stock X gave a return of 42% and Stock Y gave a return of 37%. Aakash’s total interest earnings from his investment in both the stocks was Rs 2,00,000/-. How much did he invest in stock Y?

Answer: 200000

**Explanation** :

Total earnings of Rs 2,00,000/- is 40% of 5,00,000.

So, ratio of investments in X to that of Y is 3 : 2.

Hence investment in Y is 2/5^{th} of Rs. 5,00,000 = Rs 2,00,000.

Hence, 200000.

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

Solution 1 has 52% milk. Solution 2 has 40% milk. 15 litres from the first Solution is poured into a 3rd container. What quantity (in litres) from Solution 2 should be added to the 3rd container to get a resultant solution of 44% milk?

Answer: 30

**Explanation** :

Let ‘x’ litres be the quantity of the mixture in Solution 2.

Therefore, 4/8 = 15/x

Therefore, x = 30 litres.

Hence, 30.

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

A dealer mixes cereal costing Rs. 8 per kg with cereal costing Rs. 7 per kg and sells the mixture at Rs. 8 per kg and earns a profit of $7\frac{1}{2}\%$ on his sale price. In what proportion does he mix them.

- (a)
1 : 2

- (b)
2 : 3

- (c)
3 : 4

- (d)
4 : 5

Answer: Option B

**Explanation** :

Selling Price of the mixture = Rs. 8/kg

7.5% profit is earned on selling price, hence profit = Rs. 8 × 7.5% = Rs. 0.6

∴ CP of the mixture = 8 - 0.6 = Rs. 7.4

∴ Ratio = 0.4 : 0.6 = 2 : 3

Hence, option (b).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

A 24 kg ingot contains 54% gold. Another 12 kg ingot contains 72% gold. Both these are melted together to form a new 36 kg ingot. What will be the percentage of gold in the new ingot?

Answer: 60

**Explanation** :

Let ‘x’ be the percentage of gold in the new ingot. Therefore, using rule of allegation.

Therefore, $\frac{72-X}{X-54}=\frac{24}{12}$

That gives, X = 60%

**Alternately,**

It would be better to use the weighted average approach here.

i.e. weighted average (X) = $\frac{24\times 54\%+12\times 72\%}{24+12}$

⇒ X = $\frac{2\times 54+72}{3}$ = 2 × 18 + 24 = 60%.

Hence, 60.

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

The average monthly salary of employees, consisting of officers and workers, of an organisation is Rs. 3000. The average salary of an officer is 10,000 while that of a worker is 2000 per month. If there are total 480 employees in the organisation, find the number of officers.

- (a)
60

- (b)
50

- (c)
80

- (d)
40

Answer: Option A

**Explanation** :

Ratio of officers to workers = 1000 : 7000 = 1 : 7

Number of officers = 1/8 × 480 = 60

**Alternately**,

Let the number of officers be x

Number of workers = 400 – x

⇒ 10000 × x + 2000(400 - x) =3000(400)

⇒ 10000x + 800000 - 2000x = 12,00,000

⇒ 4x = 600 - 400 = 200

⇒ x = 50

∴ Number of officers = 50

Hence, option (a).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

What amounts (in litres) of 90% and 97% pure acid solutions respectively are mixed to obtain 35 L of 95% pure acid solution?

- (a)
20 and 15 L

- (b)
25 and 10 L

- (c)
20 and 15 L

- (d)
10 and 25 L

Answer: Option D

**Explanation** :

∴ Amount of the solution x and y in ratio 2 : 5

Amount of 90% acid in solution x = 2/7 × 35 = 10L

Amount of acid in solution y = 5/7 × 35 = 25L

Hence, option (d).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

A trader has 100 kg of rice, part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4%. How much quantity is sold at 14% profit and that at 6% loss?

- (a)
10 and 90 kg

- (b)
40 and 60 kg

- (c)
90 and 10 kg

- (d)
None of these

Answer: Option A

**Explanation** :

Hence, ratio of quantity sold at 14% profit and 6% loss = 2 : 18 = 1 : 9

Hence, rice sold at 14% profit = (100 × 1)/10 = 10 kg

Rice sold at 6% loss = 90 kg.

Hence, option (a).

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**CRE 2 - Alligation | Arithmetic - Mixture, Alligation, Removal & Replacement**

In a zoo, there are Rabbits and Pigeons. If heads are counted, there are 400 and if legs are counted, there are 1120. How many pigeons are there?

- (a)
180

- (b)
200

- (c)
220

- (d)
240

Answer: Option D

**Explanation** :

Heads Count = 400.

Legs count = 1120.

Average Legs count for per head = 1120/400 = 14/5.

Rabbits : Pigeons = (4/5) : (6/5) = 2 : 3.

Number of Pigeons = (400 × 3)/5 = 240.

Hence, option (d).

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