Question: A merchant mixes three varieties of rice costing $20/kg, $24/kg and $30/kg and sells the mixture at a profit of 20% at $30/kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

1. 1 kg
2. 3 kgs
3. 5 kgs
4. 6 kgs
5. 7 kgs

“A merchant mixes three varieties of rice costing $20/kg, $24/kg” - is a subject that the GMAT quantitative reasoning section covers. A school needs to be proficient in a variety of qualitative skills to answer the GMAT Problem Solving questions correctly. There are 31 questions in the GMAT Quant section as a whole. The GMAT Quant topics' problem-solving section calls for the resolution of calculative mathematical puzzles.

Solutions and Explanation

Approach Solution : 1

Consider A=20$kg, B=24$kg, C =30$kg

Let rice A, B, and C each weigh x kg, y kg, and 2 kg, respectively.

Last CP = 25

We can calculate the cost prices as follows:

20x+24y+60 = 25(x+y+2)

Therefore y=10−5x

Since x cannot be greater than 1 and y cannot be zero or negative, x can only be 1 and thus,
y = 5 kg.

Correct Answer: (C)

Approach Solution : 2

The mixture is being sold at a profit of $ 30/kg, the cost price of the mixture will be (30/1.2) = $ 25/kg

Qa-------Qc
20-------30
-----25-----
5---------5 Ratio (1:1)

Similarly,

Qb--------Qc
24--------30
------25-----
5----------1 Ratio (5 : 1)

Now, if we combine both of these mixtures, the final mixture will contain the following amounts,

Qa = 1 kg from mixture
Qb = 5 kg from mixture 2
Qc = 1 kg from mixture 1 and 1 kg from mixture 2.

The mixture is added in the following proportions: 1: 5: 2

Since the third variety mixture is already included in the question at a weight of 2 kg, the second variety is 5 kg.

Correct Answer: (C)

Approach Solution : 3

He makes a 20% profit when he sells the mixture for 30 rupees per kilogramme. Thus, the cost price of that mixture is 30/1.2 = 25 rupees per kilogramme.

To create a mixture with a price of Rs. 25/kg, first combine the varieties 1 and 3.
Apply Alligation,

Therefore, varieties 1 and 3 must be used in a 1 : 1 ratio.

Combine varieties 2 and 3 to create a mixture with a price of Rs. 25/kg.

Variety 1: variety 3 = to 1: 1.

Variety 3: Variety 2 = 5: 1

Therefore, the necessary ratio for mixing all three is 1: 5: 2.

Second variety must be 5 kg if the third variety weighs 2 kg.

Correct Answer: (C)

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