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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-7 section-1

61
The ratio of the quantities of sugar, in which sugar costing Rs. 20 per kg and Rs. 15 per kg, should be mixed so that here will be neither loss nor gain on selling the mixed sugar at the rate of Rs. 16 per kg, is -
Discuss
Answer & Solution
Answer: Option D
Solution:
According to the question,
When there is no profit no loss,
Here, Cost price = Selling price
∴ Cost price of mixed sugar = Rs. 16/kg
Apply alligation
Alligation mcq solution image
$$ \Rightarrow {\text{Ratio }} \to 1:4$$
62
The proportion of acid and water in three samples is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and acid in the mixture is -
Discuss
Answer & Solution
Answer: Option D
Solution:
According to the question,

\[\begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Acid}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Water}}\,\,\,\,\,\,{\text{Total}} \hfill \\ \left. \begin{gathered} {\text{Sample I}}\,\,\,\,\,\,\,\,{{\text{2}}_{ \times 40}} = 80\,\,\,\,:\,\,\,\,{1_{ \times 40}} = 40\,\,\,\,\,\,{3_{ \times 40}} \hfill \\ \hfill \\ {\text{Sample II}}\,\,\,\,\,\,{3_{ \times 24}} = 72\,\,\,\,\,:\,\,\,\,{2_{ \times 24}} = 48\,\,\,\,{5_{ \times 24}} \hfill \\ \hfill \\ {\text{Sample III}}\,\,\,\,\,\underline {{5_{ \times 15}} = 75} \,\,\,\,:\,\,\,\,\,\underline {{3_{ \times 15}} = 45} \,\,\,\,{8_{ \times 15}} \hfill \\ \end{gathered} \right]120 \hfill \\ \end{gathered} \]

\[{\text{Ratio of quantity }}\boxed{\,\,\,227\,\,\,\,\,:\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,133\,\,\,}\]
$${\text{Required ratio = }}133:227$$
63
A shopkeeper bought 15 kg of rice at the rate of Rs. 29 per kg and 25 kg of rice at the rate of Rs. 20 per kg. He sold the mixture of both types of rice at the rate of Rs. 27 per kg. His profit in this transaction is -
Discuss
Answer & Solution
Answer: Option D
Solution:
According to the question,
Cost price of the mixture
= 15 × 29 + 25 × 20
= Rs. 935
Selling price of the mixture
= 27 × 40
= Rs. 1080

Profit = Selling price - Cost price
Profit = 1080 - 935 = Rs. 145
64
Lala has lent some money to Arun at 5% p.a. and Bhatia at 8% p.a. At the end of the year, he has gained an overall interest at the rate 6%. In what ratio has he lent the money to Arun and Bhatia ?
Discuss
Answer & Solution
Answer: Option A
Solution:
By alligation method -
Alligation mcq solution image
Then, Lala give loan in ratio 2 : 1, to Arun and Bhatia
65
The ratio of milk and water in mixture of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4 respectively. In which container is the quantity of milk, relative to water, minimum ?
Discuss
Answer & Solution
Answer: Option C
Solution:
∴According to the question,
Container :
$$\eqalign{ & \,\,\,\,\,\,\,\,{\text{I}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{II}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{III}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{IV}} \cr & {\text{M}}\,:\,{\text{W}}\,\,\,{\text{M}}\,:\,{\text{W}}\,\,\,{\text{M}}\,:\,{\text{W}}\,\,\,{\text{M}}\,:\,{\text{W}} \cr & \,\,\,\,5:3\,\,\,\,\,\,\,\,\,\,\,2:1\,\,\,\,\,\,\,\,\,\,\,3:2\,\,\,\,\,\,\,\,\,\,7:4 \cr} $$

$$\eqalign{ & {\bf{Container}}\,\,({\text{I}}): \cr & \frac{{{\text{Milk}}}}{{{\text{Water}}}} = \frac{5}{3} = 1.67 \cr & \cr & {\bf{Container}}\,\,({\text{II}}): \cr & \frac{{{\text{Milk}}}}{{{\text{Water}}}} = \frac{2}{1} = 2 \cr & \cr & {\bf{Container}}\,\,({\text{III}}): \cr & \frac{{{\text{Milk}}}}{{{\text{Water}}}} = \frac{3}{2} = 1.5 \cr & \cr & {\bf{Container}}\,\,({\text{IV}}): \cr & \frac{{{\text{Milk}}}}{{{\text{Water}}}} = \frac{7}{4} = 1.75 \cr} $$

∴ The quantity of milk relative to water minimum in container third.
66
In two types of stainless steel, the ratio of chromium and steel are 2 : 11 and 5 : 21 respectively. In what proportion should the two types be mixed so that the ratio of chromium to steel in the mixed type becomes 7 : 32 ?
Discuss
Answer & Solution
Answer: Option C
Solution:
According to the question,
\[\begin{gathered} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Chromium}}\,\,{\text{Steel}} \hfill \\ {\text{Type 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,\,:\,\,\,\,\,11 \hfill \\ {\text{Type 2}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5\,\,\,\,{\text{:}}\,\,\,\,\,\,\,21 \hfill \\ \end{gathered} \]
Now using alligation,
Alligation mcq solution image
\[{\text{Ratio of quantity }} \to \boxed{\,\,1\,\,\,\,\,\,:\,\,\,\,\,\,2\,\,}\]
67
Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of mixture of spirit and water. In the 1st container the ratio of spirits and water is 4 : 1, in 2nd container the ratio is 11 : 4 and on the 3rd container ratio is 7 : 3. All the three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is ?
Discuss
Answer & Solution
Answer: Option C
Solution:
In 2 litres of first container,
Spirit = $$2 \times \frac{4}{5} = \frac{8}{5}$$
water = $$2 \times \frac{1}{5} = \frac{2}{5}$$

In 3 litres of first container,
Spirit =$$3 \times \frac{11}{15} = \frac{11}{5}$$
water = $$3 \times \frac{4}{15} = \frac{4}{5}$$

In 4 litres of first container,
Spirit =$$4 \times \frac{7}{10} = \frac{14}{5}$$
water = $$4 \times \frac{3}{10} = \frac{6}{5}$$

∴ Required ratio
$$ = \left( {\frac{8}{5} + \frac{{11}}{5} + \frac{{14}}{5}} \right) : \left( {\frac{2}{5} + \frac{4}{5} + \frac{6}{5}} \right) $$
$$ = \frac{{33}}{5} : \frac{{12}}{5} $$
= 33 : 12
= 11 : 4
68
Alcohol and water in two vessels A and B are in the ratio 5 : 3 and 5 : 4 respectively. In what ratio, the liquid of both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7 : 5 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
According to the question,
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Alcohol}}\,\,\,\,\,\,{\text{Water}} \cr & {\text{Vessel A}}\,\,\,\,\,\,\,\,5\,\,\,\,:\,\,\,\,\,{\text{3}} \cr & {\text{Vessel B}}\,\,\,\,\,\,\,\,5\,\,\,\,{\text{:}}\,\,\,\,\,4 \cr} $$
Now using alligation,
Alligation mcq solution image
69
Two vessels A and B contains acid and water in the ratio 4 : 3 and 5 : 3 respectively. Then the ratio in which these mixtures to be mixed to obtain a new mixture in vessel C containing acid and water in the ratio 3 : 2 is -
Discuss
Answer & Solution
Answer: Option B
Solution:
According to the question,
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Acid}}\,\,\,\,\,\,\,{\text{Water}} \cr & {\text{Vessel A}}\,\,\,\,\,{\text{4}}\,\,\,\,:\,\,\,\,{\text{3}} \cr & {\text{Vessel B}}\,\,\,\,\,\,{\text{5}}\,\,\,\,{\text{:}}\,\,\,\,\,{\text{3}} \cr} $$
Now using alligation,
Alligation mcq solution image
70
The ratio of spirit and water in two mixtures of 20 litres and 36 litres is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Mixture }} - {\text{1 = 20 litres}} \cr & {\text{Mixture }} - {\text{2 = 36 litres}} \cr & {\text{In Mixture }} - {\text{1 ratio of }} \cr & {\text{ }}\frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \left. {\frac{3}{7}} \right\rangle 10{\text{ units}} \cr & {\text{In Mixture }} - 2{\text{ ratio of}} \cr & {\text{ }}\frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \left. {\frac{7}{5}} \right\rangle 12{\text{ units}} \cr & \cr & {\text{10 units }} \to {\text{20 litres}} \cr & \,\,\,{\text{1 unit }}\,\,\, \to {\text{2 litres}} \cr & {\text{12 units }} \to {\text{36 litres}} \cr & \,\,\,{\text{1 unit }}\,\,\, \to {\text{3 litres}} \cr & \cr & \therefore {\text{In Mixture }} - {\text{1 ratio of }} \cr & \frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \frac{{3 \times 2}}{{7 \times 2}} = \frac{6}{{14}} \cr & \cr & \therefore {\text{In Mixture }} - 2{\text{ ratio of }} \cr & \frac{{{\text{Spirit}}}}{{{\text{Water}}}} = \frac{{7 \times 3}}{{5 \times 3}} = \frac{{21}}{{15}} \cr & \cr & {\text{Ratio of spirits and water}} \cr & {\text{ = }}\frac{{6 + 21}}{{14 + 15}} \cr & {\text{ = }}\frac{{27}}{{29}} \cr & {\text{ = 27:29}} \cr} $$