Question

What is the price of mangoes per kg? I. Ten kg of mangoes and two dozens of oranges cost Rs. 252.
I II. Two kg of mangoes could be bought in exchange for one dozen oranges.

• A. If the question can be answered with the help of statement I alone
• B. If the question can be answered with the help of statement II alone
• C. If both, statement I and statement II are needed to answer the question
• D. If the question cannot be answered even with the help of both the statements

Hint:

Combine equations from both statements to eliminate variables and solve for the unknown.

Answer 1

The Correct Option is C

Let the price of mangoes be \( x \) rupees per kg and the price of oranges be \( y \) rupees per dozen.
From Statement I: Ten kg of mangoes and two dozen oranges cost Rs. 252. So we get: \[ 10x + 2y = 252 \tag{1} \] This is a linear equation in two variables \( x \) and \( y \), so we cannot determine the value of \( x \) alone.
From Statement II: Two kg of mangoes = one dozen oranges, in terms of value. That means: \[ 2x = y \tag{2} \] This gives a relationship between \( x \) and \( y \), but not the value of either.
Using both statements I and II: From (2), substitute \( y = 2x \) into equation (1): \[ 10x + 2(2x) = 252 10x + 4x = 252 14x = 252 x = 18 \] So, the price of mangoes per kg is \( \boxed{18 \text{ rupees}} \)