Alligations and Mixtures Quiz Set 012 | Maths Aptitude Quiz Questions and Mock Test on Alligations and Mixtures Set 12 | mock tests for Bank PO, SSC Exams, SO Clerical Exam, GATE Exam, LIC AO, GIC AO, etc.

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Question 1

A milkman has 24 liters of 12% curd, and 16 liters of 2% curd. If he mixes equal quantities of the two curd samples, then what is the percentage curd in the mixture?

8%.

9%.

7%.

11%.

Soln.
Ans: c

Quantities are equal, so answer = (12/100 + 2/100) X 100 = 7%.

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Question 2

An electronics shop sold 12 TV sets at a 23% profit, and 6 Coolers at 2% profit. What is the average percentage profit earned by the shop?

16%.

17%.

15%.

19%.

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 = 2, A₁ = 23, n1 = 12, n2 = 6, we have 12 × (A - 23) = 6 × (2 - A), from where we get A = 16%. The "property" in the alligation formula could be percentage, speed, weight, price, etc.,

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Question 3

A mixture of milk and water contains 14 parts of milk and 9 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?

${5/28}$.

$1{2/9}$.

$2{1/30}$.

$2{29/30}$.

Soln.
Ans: a

Let the volume of the mixture be 14 + 9 = 23 liters. If x liters of the mixture is removed and replaced by water, the volume of water in the new mixture is $9 - {9x}/23 + x$. The volume of the milk in the new mixture would be $14 - {14x}/23.$ Equating the two volumes and solving for x we get x = ${23 × 5}/{2 × 14}$. The fraction that must be removed = $1/23$ × ${23 × 5}/{2 × 14}$, which gives $5/{2 × 14}$ = ${5/28}$.

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Question 4

In what ratio should water and wine be mixed so that after selling the mixture at cost price a profit of 25% is made?

${1/4}$.

$1{2/3}$.

$1{1/2}$.

$2{1/6}$.

Soln.
Ans: a

The water will be sold at the price of wine. So the profit will be earned by selling water as wine. Profit% = $\text"Profit"/\text"Cost"$ × 100. If profit percent is 25%, then 1 part of pure water is sold at the cost of 4 parts of wine. So the required mixing ratio should be 1 : 4.

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Question 5

The average weight of a class of 20 students is 3 Kg, and the average weight of a class of 40 students is 9 Kg. What is the average weight of the two combined classes?

7 Kg.

8 Kg.

6 Kg.

10 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 = 20, A₁ = 3, n₂ = 40 and A₂ = 9, we get A = 7 Kg.