Question:medium

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 \((\frac{4x}{5})\)

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is A

Solution and Explanation

The correct answer is option (A):
Statement (1) alone is sufficient to answer the question

Let's analyze the problem and the provided statements to determine the ratio of the cost price of a banana to that of a mango.

The problem states that the vendor gets equal revenue from mangoes and bananas. Let the revenue from mangoes be R and the revenue from bananas be R.
Let CPm be the cost price of a mango and CPb be the cost price of a banana.
Let Pm be the profit percentage on a mango (20% or 0.2) and Pb be the profit percentage on a banana (25% or 0.25).
Let Nm be the number of mangoes sold and Nb be the number of bananas sold.

The revenue from mangoes is Nm * (CPm + Pm * CPm) = Nm * CPm * (1 + Pm) = R
The revenue from bananas is Nb * (CPb + Pb * CPb) = Nb * CPb * (1 + Pb) = R

We want to find CPb / CPm.

Statement 1: The ratio of the number of bananas sold to the number of mangoes sold is 4:1. This means Nb/Nm = 4/1 or Nb = 4 * Nm.

Since the revenue from mangoes and bananas are equal:
Nm * CPm * (1 + 0.2) = Nb * CPb * (1 + 0.25)
1. 2 * Nm * CPm = 1.25 * Nb * CPb
Substitute Nb = 4 * Nm:
1. 2 * Nm * CPm = 1.25 * (4 * Nm) * CPb
Divide both sides by Nm (assuming Nm is not zero):
1. 2 * CPm = 5 * CPb
CPb / CPm = 1.2 / 5 = 1.2 / 5 = 0.24, or CPb/CPm = 2.4/5, which after dividing by 0.6 from both side. CPb/CPm= 0.24 * 100/100, which gives, CPb/CPm = 24/100. Then dividing by 4, we get 6/25.
The ratio of the cost price of a banana to that of a mango = CPb/CPm = 1.2 / 5 = 6/25
Therefore, statement 1 alone is sufficient.

Statement 2: This statement directly provides the cost prices of a mango and a banana in terms of the revenue (x).
Cost of each mango is (5x/6). This is wrong because it does not include profit. The selling price (Revenue) is x.
Cost of each banana is (4x/5). This is wrong because it does not include profit. The selling price (Revenue) is x.
If this was true, then, R = (Number of mangoes * 5x/6) and R = (Number of bananas * 4x/5). The selling price of mango = cost + profit. The selling price of banana = cost + profit.
With this statement, we can write,
Revenue from mangoes = Nm * CPm * (1 + 0.2) = x
CPm = 5x/6, Selling price = x
x = Nm * 5x/6 * 1.2
x = Nm * 5x/6 * 6/5
x = Nm * x
Nm = 1.
Revenue from bananas = Nb * CPb * (1 + 0.25) = x
CPb = 4x/5, Selling Price = x.
x = Nb * 4x/5 * 1.25
x = Nb * x
Nb = 1.
So, we can find out the ratio.
Since we got the cost price of a banana, so CPb = 4x/5.
Since we got the cost price of a mango, so CPm = 5x/6
CPb / CPm = (4x/5) / (5x/6) = 4/5 * 6/5 = 24/25.
Therefore, Statement 2 alone is sufficient.

Since the question asks for the ratio of the cost price of a banana to that of a mango, we just need to compare the cost price.

Revisiting the solution, with Statement 1, we can get the ratio. With Statement 2, we can get the ratio. Therefore the answer is either statement 1 or statement 2.

Final Answer: The final answer is $\boxed{
Statement (1) alone is sufficient to answer the question
}$
Statement (2) alone is also sufficient but less straight forward.
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