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Alligation - Aptitude MCQ Questions and Solutions with Explanations

Alligation MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Alligation with easy and logical explanations. Alligation MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-9 section-1

81
Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio 1 : 2 : 3. If the mixture is worth Rs. 75 per kg, then the price of the third variety per kg will be equal to:
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Let third variety}} = x \cr & 80\,\,:\,\,50\,\,:\,\,x \cr & \,\,1\,\,\,:\,\,\,\,2\,\,\,:\,\,\,3 \cr & \overline {\,80 + 100 + 3x\,} = \left( {3 + 2 + 1} \right) \times 75 \cr & 180 + 3x = 6 \times 75 \cr & 3x = 270 \cr & x = 90{\text{ per kg}} \cr} $$
82
A container contains 25 litre of milk. From this container, 5 litre of milk is taken out and replaced by water. This process is further repeated two times. How much milk is there in the container now?
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & {\text{Final quantity}} = {\text{Initial quantity}}{\left( {1 - \frac{{{\text{Quantity take out}}}}{{{\text{Capacity of vessel}}}}} \right)^{{\text{Number of process}}}} \cr & = 25{\left( {1 - \frac{5}{{25}}} \right)^3} \cr & = 25{\left( {1 - \frac{1}{5}} \right)^3} \cr & = 25 \times \frac{4}{5} \times \frac{4}{5} \times \frac{4}{5} \cr & = 12.8{\text{ litre}} \cr} $$
83
A container has 20% milk and 80% water in it. It is mixed with another sample (inequal quantity) having 80% milk and 20% water. What would be the milk content in the final mixture?
Discuss
Answer & Solution
Answer: Option C
Solution:
\[\begin{array}{*{20}{c}} {}&{{\text{Milk}}}&{{\text{Water}}}&{} \\ {}&{20}&{80}&{ = 100} \\ {{\text{New, mixture}}}&{\frac{{80}}{{100}}}&{\frac{{20}}{{100}}}&{ = 100} \\ {}&{50}&{50}&{ = 100} \end{array}\]
$${\text{Milk}} = 50\% {\text{ Answer}}$$
84
A jar contains a blend of a fruit juice and water in the ratio 5 : x. When 1 litre of water is added to 4 litres of the blend the ratio of fruit juice to water becomes 1 : 1. What is the value of x?
Discuss
Answer & Solution
Answer: Option A
Solution:
New mixture = Original mixture + Added water
= 4 + 1
= 5 Ltr
Alligation mcq question image
After comparing x = 3
85
The ratio of milk to water in a 100 litres mixture is 2 : 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times. What is the percentage of milk in final mixture?
Discuss
Answer & Solution
Answer: Option D
Solution:
\[\begin{array}{*{20}{c}} {{\text{Milk}}}&{}&{{\text{Water}}}&{} \\ \begin{gathered} 2 \hfill \\ \downarrow \hfill \\ \end{gathered} &\begin{gathered} : \hfill \\ \hfill \\ \end{gathered} &\begin{gathered} 3 \hfill \\ \downarrow \hfill \\ \end{gathered} &\begin{gathered} = 5 \to 100 \hfill \\ \,\,\,1 \to 20 \hfill \\ \end{gathered} \\ {40}&{}&{60}&{} \end{array}\]
$$\eqalign{ & = 60{\left( {1 - \frac{{10}}{{100}}} \right)^3}\% \cr & = 60{\left( {\frac{9}{{10}}} \right)^3}\% \cr & = 60 \times \frac{{729}}{{1000}}\% \cr & = 43.74\% \cr & \therefore {\text{Final milk }}\% = \left( {100 - 43.74} \right)\% \cr & = 56.26\% \cr} $$
86
If X beakers of 100 ml containing 1 : 4 acid-water solution are mixed with Y beakers of 200 ml containing 3 : 17 acid-water solution then the ratio of acid to water in the resulting mixture becomes 19 : 91. Find X : Y.
Discuss
Answer & Solution
Answer: Option A
No explanation is given for this question. Let's Discuss on Board
87
A mixture of milk and water measures 60 litres. It contains 10% water. How much water should be added to it, so that the water may be 25%?
Discuss
Answer & Solution
Answer: Option D
Solution:
\[\begin{array}{*{20}{c}} {\,\,\,\,\,\,\,\,\,\,10\% }&{}&{100\% } \\ {}&{\,\,\,\,\,\,\,\,\,\,\,\,\,25\% }&{} \\ {\,\,\,\,\,\,\,\,\,\,75\% }&{}&{15\% } \\ {60 \leftarrow 5\,\,}&{\,\,\,\,\,\,\,\,\,\,\,:}&{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1 \to 12{\text{ litres}}} \end{array}\]
88
A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution of contain 25% sulphuric acid.
Discuss
Answer & Solution
Answer: Option C
Solution:
Alligation mcq question image
89
A mixture is composed of 11 parts of pure milk and 2 parts of water. If 35 litres of water were added to the mixture then the new mixture will contain twice as much pure milk as water, then how many litres of pure milk does the original mixture contain?
Discuss
Answer & Solution
Answer: Option A
Solution:
\[\begin{array}{*{20}{c}} {{\text{Original mixture}}}&{{\text{Milk}}}&{}&{{\text{Water}}} \\ {}&{11}&:&2 \\ {}&2&:&1 \end{array}\]
Alligation mcq question image
So, the quantity of milk in original mixture is 22 unit × 5 Ltr. = 110 Ltr.
90
An alloy is made by mixing metal A costing Rs. 2000 per kg and metal B costing Rs. 400 per kg in the ratio A : B = 3 : 1. What is the cost (in Rs.) of 8 kg of this alloy?
Discuss
Answer & Solution
Answer: Option D
Solution:
Metal A = 2000 per kg
Metal B = 400 per kg
Alligation mcq question image
∴ Cost of 8 kg of alloy = By mixing 6 kg metal A and 2 kg metal B
Cost = 6 × 2000 + 2 × 400 = Rs. 12,800