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Question: A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage.
- The rate of X is Rs. 20 per kg.
- The rate of Y is Rs. 13 per kg.
A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.
Approach Solution 1
- The rate of X is Rs. 20 per kg.
This statement provides the rate of rice X but does not provide any information about the quantity of X used in the mixture or the quantity of Y. Without the quantity information, we cannot calculate the cost price or the profit percentage.
- The rate of Y is Rs. 13 per kg.
This statement provides the rate of rice Y but, similar to statement I, does not provide any quantity information. Without the quantity information, we cannot calculate the cost price or the profit percentage.
E is the correct answer.
Approach Solution 2
The cost of x kg of rice X at a rate of Rs. 20 per kg is 20x.
The cost of y kg of rice Y at a rate of Rs. 13 per kg is 13y.
The total cost price of the mixture is 20x + 13y.
The selling price of the mixture is Rs. 17 per kg. Therefore, the selling price of (x + y) kg of the mixture is 17(x + y).
Profit = Selling Price - Cost Price
Profit = 17(x + y) - (20x + 13y)
Profit = 17x + 17y - 20x - 13y
Profit = -3x + 4y
To find the profit percentage, we need to calculate the profit percentage relative to the cost price:
Profit Percentage = (Profit / Cost Price) × 100
Profit Percentage = [( -3x + 4y ) / (20x + 13y)] × 100
Now, let's consider the statements:
- The rate of X is Rs. 20 per kg.
This statement provides the rate of rice X, which is Rs. 20 per kg. However, it does not provide any information about rice Y or the quantities of rice X and Y used. So, statement I alone is not sufficient to calculate the profit percentage.
- The rate of Y is Rs. 13 per kg.
This statement provides the rate of rice Y, which is Rs. 13 per kg. Similar to statement I, it does not provide any information about rice X or the quantities of rice X and Y used.
Therefore,statement II alone is not sufficient to calculate the profit percentage.
Combining both statements, we still do not have any information about the quantities of rice X and Y used. Therefore, even when considered together, the statements are not sufficient to calculate the profit percentage.
Hence, the correct answer is (E) Statements (1) and (2) TOGETHER are not sufficient.
Approach Solution 3
Let's assume that the man mixes x kg of rice X and y kg of rice Y.
The total cost price of the mixture is given by the sum of the cost of rice X and the cost of rice Y:
Cost Price = (Cost of X) + (Cost of Y) = (20x) + (13y)
The selling price of the mixture is Rs. 17 per kg, and the total weight of the mixture is (x + y) kg. Therefore, the selling price of the mixture is:
Selling Price = 17(x + y)
Profit = Selling Price - Cost Price
Profit = 17(x + y) - (20x + 13y)
Profit = 17x + 17y - 20x - 13y
Profit = -3x + 4y
Now, to determine the profit percentage, we need the profit and cost price in terms of percentages.
Profit Percentage = (Profit / Cost Price) × 100
Profit Percentage = ((-3x + 4y) / (20x + 13y)) × 100
In this case, we do not have specific values for x and y, so we cannot determine the exact profit percentage.
Therefore, the answer remains the same: (E) Statements (1) and (2) TOGETHER are not sufficient to calculate the profit percentage.
“A man mixes two types of rice (X and Y) and sells the mixture at the" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.
To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.
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