# Alligations and Mixtures Quiz Set 007

### Question 1

The average weight of a class of 80 students is 11 Kg, and the average weight of a class of 160 students is 11 Kg. What is the average weight of the two combined classes?

A

11 Kg.

B

12 Kg.

C

10 Kg.

D

14 Kg.

Soln.
Ans: a

If a sample n1 has a weighted average of A1, and another sample n2 has a weighted average of A2, then the weighted average, A,of the combined samples is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). Putting n1 = 80, A1 = 11, n2 = 160 and A2 = 11, we get A = 11 Kg.

### Question 2

In what ratio should a vendor mix two types of pulses costing Rs. 16/Kg and Rs. 21/Kg respectively so as to get a mixture of Rs. 18/Kg?

A

\$1{1/2}\$.

B

\$2{1/2}\$.

C

\$3{1/2}\$.

D

\$2{1/4}\$.

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 = 16, A = 18 we have n1 × (18 - 16) = n2 × (21 - 18), from where we get the required ratio as \$n_1/n_2 = 3 : 2\$.

### Question 3

A milkman has 4 liters of 23% curd, and 24 liters of 9% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

A

16%.

B

12%.

C

10%.

D

14%.

Soln.
Ans: a

Quantities are equal, so answer = (23/100 + 9/100) X 100 = 16%.

### Question 4

The average weight of the students of a class is 4 Kg, and the average weight of the students of another class is 14 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 13 Kg?

A

\${1/9}\$.

B

\$1{1/4}\$.

C

\$1{8/11}\$.

D

\$2{6/11}\$.

Soln.
Ans: a

If a sample n1 has a weighted average of A1, and another sample n2 has a weighted average of A2, then the weighted average, A,of the combined samples is determined by the alligation formula as: n1(A - A1) = n2(A2 - A). So the ratio is \${A_2 - A}/{A - A_1 }\$. Putting A2 = 14, A1 = 4, and A = 13, we have \${14 - 13}/{13 - 4 }\$, from where we get the ratio as \${1/9}\$.

### Question 5

12 liters of Petrol costing Rs. 5/liter is mixed with 6 liters of Kerosene costing Rs. 14/liter. What is the price of the mixture per liter?

A

Rs. 8 per liter.

B

Rs. 9 per liter.

C

Rs. 7 per liter.

D

Rs. 11 per liter.

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 = 14, A1 = 5, n1 = 12, n2 = 6, we have 12 × (A - 5) = 6 × (14 - A), from where we get A = Rs. 8 per liter. This Blog Post/Article "Alligations and Mixtures Quiz Set 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2020-02-07. Published on: 2016-05-07