# Alligations and Mixtures Quiz Set 009

### Question 1

9 Kg of Grade I sugar costing Rs. 6/Kg is mixed with 12 Kg of Grade II sugar costing Rs. 20/Kg. What is the price of the mixture per Kg?

A

Rs. 14 per Kg.

B

Rs. 15 per Kg.

C

Rs. 13 per Kg.

D

Rs. 17 per Kg.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 20, A1 = 6, n1 = 9, n2 = 12, we have 9 × (A - 6) = 12 × (20 - A), from where we get A = Rs. 14 per Kg.

### Question 2

Mr. X travels 6 km at a speed of 18 km/h, and 3 km at a speed of 15 km/h. What is the average speed during the entire journey?

A

17 km/h.

B

18 km/h.

C

16 km/h.

D

20 km/h.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average property of A1, and another sample n2 has an average property of A2, then the average property of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 15, A1 = 18, n1 = 6, n2 = 3, we have 6 × (A - 18) = 3 × (15 - A), from where we get A = 17 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,

### Question 3

3 Kg of Grade I sugar costing Rs. 13/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 21/Kg. What is the price of the mixture per Kg?

A

Rs. 19 per Kg.

B

Rs. 20 per Kg.

C

Rs. 18 per Kg.

D

Rs. 22 per Kg.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average price of A1, and another sample n2 has an average price of A2, then the price of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 21, A1 = 13, n1 = 3, n2 = 9, we have 3 × (A - 13) = 9 × (21 - A), from where we get A = Rs. 19 per Kg.

### Question 4

A 150 liter mixture of milk and water contains 82% milk. How many more liters of water should be added so that the proportions of milk and water become equal?

A

96 liter.

B

97 liter.

C

95 liter.

D

99 liter.

Soln.
Ans: a

The volume of milk will remain same at \${82 × 150}/100\$ = 123 liters. The amount of water at present is 150 - 123 = 27 liters. We need to make the volume of water equal to that of the milk. So we have to add 123 - 27 = 96 liters of water.

### Question 5

An electronics shop sold 16 TV sets at a 20% profit, and 4 Coolers at 5% profit. What is the average percentage profit earned by the shop?

A

17%.

B

18%.

C

16%.

D

20%.

Soln.
Ans: a

We shall use the alligation formula. If a sample n1 has an average property of A1, and another sample n2 has an average property of A2, then the average property of the mixture, A, is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting A2 = 5, A1 = 20, n1 = 16, n2 = 4, we have 16 × (A - 20) = 4 × (5 - A), from where we get A = 17%. The "property" in the alligation formula could be percentage, speed, weight, price, etc., 