Question

My son adores chocolates. He likes biscuits. But he hates apples. I told him that he can buy as many chocolates as he wishes. But then he must have biscuits twice the number of chocolates and should have apples more than biscuits and chocolates together. Each chocolate costs Rs. 1. The cost of an apple is twice the chocolate and four biscuits are worth one apple. Then which of the following can be the amount that I spent on that evening on my son if the number of chocolates, biscuits, and apples bought were all integers?

• A. Rs. 34
• B. Rs. 33
• C. Rs. 8
• D. None of these

Hint:

For problems involving costs and quantities, use the given relationships to express all quantities in terms of one variable, and check for consistency with the total cost.

Answer 1

The Correct Option is A

Let the number of chocolates be \( C \), the number of biscuits be \( B \), and the number of apples be \( A \). The problem gives the following conditions: 1. The number of biscuits is twice the number of chocolates: \[ B = 2C. \] 2. The number of apples is greater than the number of biscuits and chocolates together: \[ A > B + C. \] 3. The cost of each chocolate is Rs. 1, so the cost of chocolates is \( C \times 1 = C \) rupees. 4. The cost of each apple is twice the cost of a chocolate, so the cost of apples is \( 2A \) rupees. 5. Four biscuits are worth one apple, so the cost of biscuits is \( \frac{B}{4} \times 2A = \frac{B}{2} \) rupees. The total amount spent is: \[ \text{Total cost} = C + 2A + \frac{B}{2}. \] Now, substitute \( B = 2C \) into the total cost equation: \[ \text{Total cost} = C + 2A + \frac{2C}{2} = C + 2A + C = 2C + 2A. \] Now, solve for the number of chocolates, biscuits, and apples. We can check the given options to find that the total cost is Rs. 34. Thus, the correct answer is Rs. 34.