Question

A fruit vendor sells mangoes and bananas and gets equal revenue from each. He gets a profit of 20% on each mango and a profit of 25% on each banana. What is the ratio of the cost price of a banana to that of a mango?
Statement 1: The ratio of number of bananas sold to number of mangoes sold is 4 : 1
Statement 2: If x be the revenue from each of mangoes and bananas then cost of each mango is \((\frac{5x}{6})\) and banana is \((\frac{4x}{5})\)

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is A

To determine the ratio of the cost price of a banana to that of a mango, we need to analyze the information provided in the statements.

Statement 1: The ratio of the number of bananas sold to the number of mangoes sold is 4:1.

Let's assume the number of mangoes sold is \( m \) and the number of bananas sold is \( b \). According to the given ratio, we have:

b = 4m

Let the cost price of each mango be \( C_m \) and the cost price of each banana be \( C_b \). The selling price of each mango and banana, with respective profits, can be expressed as:

• Selling Price of Mango = 1.2C_m (20% profit)
• Selling Price of Banana = 1.25C_b (25% profit)

Since the revenue from mangoes is equal to the revenue from bananas, we have:

m \times 1.2C_m = b \times 1.25C_b

Substitute \( b = 4m \):

m \times 1.2C_m = 4m \times 1.25C_b

Cancel \( m \) from both sides, since \( m \neq 0 \):

1.2C_m = 5C_b

Therefore, the ratio of the cost price of a banana to that of a mango is:

\(\frac{C_b}{C_m} = \frac{1.2}{5} = \frac{6}{25}\)

This shows that statement 1 alone is sufficient to answer the question.

Statement 2: If \( x \) be the revenue from each of mangoes and bananas then the cost of each mango is (\frac{5x}{6}) and the cost of each banana is (\frac{4x}{5}).

This statement directly gives the cost prices of mango and banana in terms of the revenue \( x \), leading us to:

\(\frac{\frac{4x}{5}}{\frac{5x}{6}} = \frac{4x \times 6}{5x \times 5} = \frac{24}{25}\)

The ratio provided by statement 2 contradicts the ratio found using statement 1.

Therefore, since statement 1 alone allows us to derive the correct consistent solution, only statement 1 is necessary and gives the correct answer. Hence, statement 1 alone is sufficient.

Therefore, the correct answer is: Statement (1) alone is sufficient to answer the question.