# Alligations and Mixtures Quiz Set 006

### Question 1

In what ratio should a vendor mix two types of pulses costing Rs. 19/Kg and Rs. 4/Kg respectively so as to get a mixture of Rs. 14/Kg?

A

2.

B

3.

C

4.

D

\$1{2/3}\$.

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 = 4, A1 = 19, A = 14 we have n1 × (14 - 19) = n2 × (4 - 14), from where we get the required ratio as \$n_1/n_2 = 2 : 1\$.

### Question 2

18 Kg of Grade I sugar costing Rs. 7/Kg is mixed with 9 Kg of Grade II sugar costing Rs. 16/Kg. What is the price of the mixture per Kg?

A

Rs. 10 per Kg.

B

Rs. 11 per Kg.

C

Rs. 9 per Kg.

D

Rs. 13 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 = 16, A1 = 7, n1 = 18, n2 = 9, we have 18 × (A - 7) = 9 × (16 - A), from where we get A = Rs. 10 per Kg.

### Question 3

Mr. X travels 8 km at a speed of 23 km/h, and 16 km at a speed of 17 km/h. What is the average speed during the entire journey?

A

19 km/h.

B

20 km/h.

C

18 km/h.

D

22 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 = 17, A1 = 23, n1 = 8, n2 = 16, we have 8 × (A - 23) = 16 × (17 - A), from where we get A = 19 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,

### Question 4

A mixture of milk and water contains 47 parts of milk and 6 parts of water. How much fraction of the mixture should be removed and replaced by water so that ratio of water and milk becomes equal?

A

\${41/94}\$.

B

\$1{14/31}\$.

C

\$2{37/96}\$.

D

\$3{35/96}\$.

Soln.
Ans: a

Let the volume of the mixture be 47 + 6 = 53 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is \$6 - {6x}/53 + x\$. The volume of the milk in the new mixture would be \$47 - {47x}/53.\$ Equating the two volumes and solving for x we get x = \${53 × 41}/{2 × 47}\$. The fraction that must be removed = \$1/53\$ × \${53 × 41}/{2 × 47}\$, which gives \$41/{2 × 47}\$ = \${41/94}\$.

### Question 5

12 Kg of Grade I sugar costing Rs. 23/Kg is mixed with 4 Kg of Grade II sugar costing Rs. 11/Kg. What is the price of the mixture per Kg?

A

Rs. 20 per Kg.

B

Rs. 21 per Kg.

C

Rs. 19 per Kg.

D

Rs. 23 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 = 11, A1 = 23, n1 = 12, n2 = 4, we have 12 × (A - 23) = 4 × (11 - A), from where we get A = Rs. 20 per Kg. 