# Alligations and Mixtures Quiz Set 002

### Question 1

The average weight of the students of a class is 3 Kg, and the average weight of the students of another class is 9 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 7 Kg?

A

\${1/2}\$.

B

\$1{1/2}\$.

C

\$2{1/2}\$.

D

\$1{3/4}\$.

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 = 9, A1 = 3, and A = 7, we have \${9 - 7}/{7 - 3 }\$, from where we get the ratio as \${1/2}\$.

### Question 2

An electronics shop sold 6 TV sets at a 10% profit, and 10 Coolers at 18% profit. What is the average percentage profit earned by the shop?

A

15%.

B

16%.

C

14%.

D

18%.

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 = 18, A1 = 10, n1 = 6, n2 = 10, we have 6 × (A - 10) = 10 × (18 - A), from where we get A = 15%. The "property" in the alligation formula could be percentage, speed, weight, price, etc.,

### Question 3

In what ratio should a vendor mix two types of pulses costing Rs. 23/Kg and Rs. 5/Kg respectively so as to get a mixture of Rs. 11/Kg?

A

\${1/2}\$.

B

\$1{1/2}\$.

C

\$2{1/2}\$.

D

\$1{3/4}\$.

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 = 5, A1 = 23, A = 11 we have n1 × (11 - 23) = n2 × (5 - 11), from where we get the required ratio as \$n_1/n_2 = 1 : 2\$.

### Question 4

The average weight of the students of a class is 3 Kg, and the average weight of the students of another class is 12 Kg. What is the ratio of the number of students in the two classes if the combined average weight is 11 Kg?

A

\${1/8}\$.

B

\$1{2/7}\$.

C

\$1{7/10}\$.

D

\$2{1/2}\$.

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 = 12, A1 = 3, and A = 11, we have \${12 - 11}/{11 - 3 }\$, from where we get the ratio as \${1/8}\$.

### Question 5

The average weight of a class of 30 students is 2 Kg, and the average weight of a class of 60 students is 8 Kg. What is the average weight of the two combined classes?

A

6 Kg.

B

7 Kg.

C

5 Kg.

D

9 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 = 30, A1 = 2, n2 = 60 and A2 = 8, we get A = 6 Kg.