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Q #26
:

Directions: Refer the following data to answer the questions given below.

In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg and Rs.100 /kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?

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Solution:

The resultant mixture is sold at a profit of 20% at Rs.96/kg

i.e. 1.2 (cost) = Rs.96 ⇒ Cost = 96/1.2 = Rs.80 / kg.

Let the three varieties be A, B, and C costing Rs.60, Rs.75 and Rs.100 respectively.

The mean price falls between B and C.

Hence the following method should be used to find the ratio in which they should be mixed.

Step 1: 

Find out the ratio of Qa:Qc using alligation rule 

Qa/Qc=(100−80)/(80−60)=1/1

Step 2: 

Find out the ratio of Qb:Qc using alligation rule   Qb/Qc=(100−80)/(80−75)=4/1

Step 3: 

Qc, the resultant ratio of variety c can be found by adding the value of Qc in step 1 and step 2 = 1 + 1 =2.

The best way to solve a problem of this kind in CAT is to go from the answer choices as shown below

The resultant ratio Qa:Qb:Qc::1:4:2

1 kg of variety A at Rs.60 is mixed with 4 kgs of variety B at Rs.75 and 2 kgs of variety C at Rs.100.

The total cost for the 7kgs=60+(4×75)+(2×100)=60+300+200=560. 

Cost per kg of the mixture = 560/7 = 80 kgs. 

 


Q #27
:

Directions: Refer the following data to answer the questions given below.

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

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Q #28
:

Directions: Refer the following data to answer the questions given below.

How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?

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S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%. C.P. of 1 kg of mixture = Rs.100/110x 9.24= Rs. 8.40

Q #29
:

Directions: Refer the following data to answer the questions given below.

A container contains 40 litres of milk. From this container 4 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

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Explanation:

Amount of milk left after 3 operations =    [40{1 -    4/40}^3 litres

=40 x9/10x9/10    x910= 29.16 litres.


Q #30
:

Directions: Refer the following data to answer the questions given below.

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:

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