## Mixture and Alligation Practice Questions & Answers with Explanation

## Mixture and Alligation

Allegation is a rule allowing one to find the ratio in which two or more ingredients must be combined at the specified price to create a mixture of the desired amount. The segment on Mixture and Alligation Practice Questions has questions about Alligation, Mean Price, and the Allegation Law.

**Alligation:**It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.**Mean Price:**The cost of a unit quantity of the mixture is called the mean price.

**Rule of Alligation**

Ratio =(M – B)=(B – M)(A – M)(M – A)

If a vessel contains A liters of milk and if B liters of milk is withdrawn and replaced by water, and again if B liters of mixture is withdrawn and replaced by water and this operation is replaced n times in all, then

- (Quantity of milk left after the n
^{th}operation)=[(A – B)]^{n}(Initial quantity of milk)A - Quantity of milk left after n
^{th}operation = A x[A(1 – (B/A))^{n}]A - Simplified formula to calculate the quantity of milk left after n
^{th}operation = [A(1 – (B/A))^{n}]

### Practice Alligations and Mixtures Questions

**1.8 Liters of wine is drawn from a cask and then filled with water. This operation is executed three times more. The ratio of the amount of wine left in cask now to that of the water is 16:65. How much wine that barrel originally holds?**

- A) 18 liters
- B) 24 liters
- C) 32 liters
- D) 42 liters

**Answer:** Option B (24 liters)

**2. A merchant has 1000 kg of sugar, of which he sells at 8 percent profit and 18 percent profit for the remainder. Overall, he gains 14 percent. The sum sold is 18 percent profit**

- A) 400 kg
- B) 560 kg
- C) 600 kg
- D) 640 kg

**Answer:** Option C (600 kg)

**3. Type 1 rice costs Rs. 15 per kg and Rs.20 per kg is Type 2 rice. If both Type 1 and Type 2 are combined in the 2:3 ratio, then the price per kg of the combined rice variety is**

- A) Rs. 19.50
- B) Rs. 19
- C) Rs. 18
- D) Rs. 18.50

**Answer:** Option C (Rs. 18)

**4. A 150-liter wine-water mixture contains 20% water. How much should more water be added so that 25% of the new mixture becomes water?**

- A) 10 liters
- B) 20 liters
- C) 30 liters
- D) 40 liters

**Answer:** Option A (10 liters)

**5. The expenditure and savings ratio is 3: 2. If the revenue rises by 15% and the savings increase by 6%, how much more will see his spending rise?**

- A) 25
- B) 21
- C) 12
- D) 24

**Answer:** Option B (21)

**6. Find the ratio in which rice is mixed in Rs. 7.20 per kg with rice in Rs. 5.70 per kg to produce a mixture worth Rs. 6.30 per kg.**

- A) 1:3
- B) 2:3
- C) 3:4
- D) 4:5

**Answer:** Option B (2:3)

**7. When 10 liters of the mixture is taken out and replaced by kerosene, the ratio of petrol and kerosene in the container becomes 2:3. The total amount of the mixture in the container is then:**

- A) 25
- B) 30
- C) 45
- D) cannot be determined

**Answer:** Option B (30)

**8. There are 50 liters of milk in a container. From that, eight liters of milk were taken out, and water replaced. This cycle was repeated twice more. What amount of milk does the bottle now contain?**

- A) 24.52 litres
- B) 29.63 litres
- C) 28.21 litres
- D) 25.14 litres

**Answer:** Option B (29.63 liters)

**9. A vessel is filled with liquid, which includes three parts of water and five parts of syrup. How much of the mixture needs to be drained off and replaced by water, so the mixture can be half water and half syrup?**

- A) 1/3
- B) 1/4
- C) 1/5
- D) 1/7

**Answer:** Option C (1/5)

**10. A milkman sells the milk at the cost price, but mixes the water therein and thus earns 9.09%. The quantity of water in a 1-liter mixture is**

- A) 83.33 ml
- B) 90.90 ml
- C) 99.09 ml
- D) can’t be determined

**Answer:** Option A (83.33 ml)