# Alligations and Mixtures Quiz Set 004

### Question 1

8 liters of Petrol costing Rs. 2/liter is mixed with 20 liters of Kerosene costing Rs. 9/liter. What is the price of the mixture per liter?

A

Rs. 7 per liter.

B

Rs. 8 per liter.

C

Rs. 6 per liter.

D

Rs. 10 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 = 9, A1 = 2, n1 = 8, n2 = 20, we have 8 × (A - 2) = 20 × (9 - A), from where we get A = Rs. 7 per liter.

### Question 2

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 10 Kg?

A

\${2/3}\$.

B

\$2{1/2}\$.

C

\$2{2/3}\$.

D

\$2{1/5}\$.

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 = 10, we have \${14 - 10}/{10 - 4 }\$, from where we get the ratio as \${2/3}\$.

### Question 3

In what ratio should a vendor mix two types of pulses costing Rs. 5/Kg and Rs. 18/Kg respectively so as to get a mixture of Rs. 11/Kg?

A

\$1{1/6}\$.

B

\$2{3/5}\$.

C

\$2{3/8}\$.

D

\$3{1/8}\$.

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 = 18, A1 = 5, A = 11 we have n1 × (11 - 5) = n2 × (18 - 11), from where we get the required ratio as \$n_1/n_2 = 7 : 6\$.

### Question 4

Two types of petrols having the prices per liter as Rs. 2 and Rs. 21 are mixed in the ratio 22 : 16. What is the price of the mixture per liter?

A

Rs. 10 per liter.

B

Rs. 11 per liter.

C

Rs. 9 per liter.

D

Rs. 13 per liter.

Soln.
Ans: a

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 = 2, n1 = 22, n2 = 16, we have 22 × (A - 2) = 16 × (21 - A), from where we get A = Rs. 10 per liter.

### Question 5

7 liters of Petrol costing Rs. 17/liter is mixed with 21 liters of Kerosene costing Rs. 9/liter. What is the price of the mixture per liter?

A

Rs. 11 per liter.

B

Rs. 12 per liter.

C

Rs. 10 per liter.

D

Rs. 14 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 = 9, A1 = 17, n1 = 7, n2 = 21, we have 7 × (A - 17) = 21 × (9 - A), from where we get A = Rs. 11 per liter. 