1. Topics
  2. Quantitative Aptitude
  3. Alligation
Question:

A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

Options:
A.\(\frac{1}{3}\)
B.\(\frac{1}{4}\)
C.\(\frac{1}{5}\)
D.\(\frac{1}{7}\)
Answer: Option C

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.

Quantity of water in new mixture = \(\left(3-\frac{3x}{8}+x\right) liters\)

Quantity of syrup in new mixture = \(\left(5-\frac{5x}{8}\right) liters\)

So,  \(\left(3-\frac{3x}{8}+x\right)=\left(5-\frac{5x}{8}\right)\)

5x + 24 = 40 - 5x

 10x = 16

x =  \(\frac{8}{5}\)

So, part of the mixture replaced = \(\left(\frac{8}{5}\times\frac{1}{8}\right)=\frac{1}{5}\)


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More Questions Related to Quantitative Aptitude > Alligation :

Question 1.

  1. 3 gallons are drawn from a container full of wine. It is then filled with water. This process is repeated four times. The quantity of wine to water left in the container in now 6561/3439. Find the capacity of the container.

Options:
  1.    25 gallons
  2.    30 gallons
  3.    35 gallons
  4.    40 gallons
Answer: Option B
Question 2.

  1. A vessel contains a mixture of two liquids A and B in the proportion of 3 : 5. When 8 litres of mixture are drawn off and the vessel is filled with liquid B, the proportion of A and B becomes 1 : 3. How many litres of liquid was contained in the vessel initially?

Options:
  1.    24
  2.    28
  3.    32
  4.    36
Answer: Option A
Question 3.

  1. A sum of Rs 36 is divided among 40 boys and girls. Each girl gets 50 p while a boy gets an amount double to that of a girl. Find the number of girls in the school.

Options:
  1.    8
  2.    10
  3.    12
  4.    14
Answer: Option A
Question 4.

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

Options:
  1.    Rs. 169.50
  2.    Rs. 170
  3.    Rs. 175.50
  4.    Rs. 180
Answer: Option C

Since first and second varieties are mixed in equal proportions.

So, their average price = Rs.     = Rs.130.50

So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x.

By the rule of alligation, we have:

 

Cost of 1 kg of 1st kindCost of 1 kg tea of 2nd kind
Rs. 130.50 Mean Price
Rs. 153		 Rs. x
(x - 153) 22.50

 

\(\frac{x-153}{22.50}=1\) 

x - 153 = 22.50

x = 175.50

Question 5.

A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

Options:
  1.    10
  2.    20
  3.    21
  4.    25
Answer: Option C

Suppose the can initially contains 7x and 5x of mixtures A and B respectively

Quantity of A in mixture left = \(\left(7x-\frac{7}{12}\times9\right) liters=\left(7x-\frac{21}{4}\right) liters\)

Quantity of B in mixture left = \(\left(5-\frac{5}{12}\times9\right) liters=\left(5x-\frac{15}{4}\right) liters\)

So,  \(\frac{\left(7x-\frac{21}{4}\right)}{\left(5x-\frac{15}{4}\right)+9}=\frac{7}{9}\)

\(\frac{28x-21}{20x+21}=\frac{7}{9}\)

 252x - 189 = 140x + 147

 112x = 336

 x = 3.

So, the can contained 21 litres of A.

Question 6.

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

Options:
  1.    4 litres, 8 litres
  2.    6 litres, 6 litres
  3.    5 litres, 7 litres
  4.    7 litres, 5 litres
Answer: Option B

Let the cost of 1 litre milk be Re. 1

Milk in 1 litre mix. in 1st can = \(\frac{3}{4}\)  litre, C.P. of 1 litre mix. in 1st can Re   \(\frac{3}{4}\)

Milk in 1 litre mix. in 2nd can = \(\frac{1}{2}\) litre, C.P. of 1 litre mix. in 2nd can Re   \(\frac{1}{2}\)

Milk in 1 litre of final mix.= \(\frac{5}{8}\)    litre, Mean price = Re    \(\frac{5}{8}\)

By the rule of alligation, we have:

C.P. of 1 litre mixture in 1st can  =  \(\frac{3}{4}\)

C.P. of mixture in 2nd can  =  \(\frac{1}{2}\)

Main price  =  \(\frac{5}{8}\)

So, Ratio of two mixtures = \(\frac{1}{8}:\frac{1}{8}=1:1\)

So, quantity of mixture taken from each can = \(\left(\frac{1}{2}\times12\right)= 6 litres\)


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