In the previous problem (no. 8) what is the maximum possible no. of chocolates?

Options

A. 52
B. 53
C. 55
D. 60

Answer

To find the maximum possible number of chocolates that a child can buy with Rs. 120, given that he has three different kinds of chocolates costing Rs. 2, Rs. 5, and Rs. 10, we can follow these steps:

### Step 1: Understand the problem
The child has Rs. 120 to spend on chocolates that cost Rs. 2, Rs. 5, and Rs. 10. We need to maximize the number of chocolates he can buy while ensuring that he buys at least one of each kind.

### Step 2: Set up the equation
Let:
- \( x \) be the number of Rs. 2 chocolates,
- \( y \) be the number of Rs. 5 chocolates,
- \( z \) be the number of Rs. 10 chocolates.

The total cost can be expressed as:
\[ 2x + 5y + 10z = 120 \]

### Step 3: Ensure at least one of each kind
Since the child must buy at least one of each kind of chocolate, we have:
- \( x \geq 1 \)
- \( y \geq 1 \)
- \( z \geq 1 \)

### Step 4: Start with the minimum requirement
To satisfy the requirement of having at least one of each kind, we can start by buying:
- 1 chocolate of Rs. 10 (costing Rs. 10),
- 1 chocolate of Rs. 5 (costing Rs. 5),
- 1 chocolate of Rs. 2 (costing Rs. 2).

The total cost for these chocolates is:
\[ 10 + 5 + 2 = 17 \]

### Step 5: Calculate remaining money
Now, we subtract this from the total amount:
\[ 120 - 17 = 103 \]

### Step 6: Maximize the number of Rs. 2 chocolates
Since Rs. 2 chocolates are the cheapest, we should buy as many of them as possible with the remaining Rs. 103. The number of Rs. 2 chocolates we can buy is:
\[ \frac{103}{2} = 51.5 \]
Since we can only buy whole chocolates, we can buy 51 Rs. 2 chocolates.

### Step 7: Calculate total chocolates
Now, we can calculate the total number of chocolates:
- Rs. 2 chocolates: 51
- Rs. 5 chocolates: 1
- Rs. 10 chocolates: 1

Total chocolates:
\[ 51 + 1 + 1 = 53 \]

### Conclusion
The maximum possible number of chocolates that the child can buy with Rs. 120 is **53**.

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