A shopkeeper buys 144 items at 90 paise each. On the way 24 items are broken. He sells the remainder at 1.20 each. His gain percent correct to one place of decimal is:

Options

A. 0.138
B. 0.144
C. 0.148
D. 0.111

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the Cost Price (CP)
The shopkeeper buys 144 items at 90 paise each.

- **Cost Price (CP)** = Number of items × Price per item
- **CP** = 144 items × 90 paise/item

Since 1 rupee = 100 paise, we convert 90 paise to rupees:
- 90 paise = 90/100 = 0.90 rupees

Now, substituting the values:
- **CP** = 144 × 0.90 = 129.6 rupees

### Step 2: Calculate the Number of Remaining Items
On the way, 24 items are broken.

- Remaining items = Total items - Broken items
- Remaining items = 144 - 24 = 120 items

### Step 3: Calculate the Selling Price (SP)
The shopkeeper sells the remaining 120 items at 1.20 rupees each.

- **Selling Price (SP)** = Number of remaining items × Selling price per item
- **SP** = 120 items × 1.20 rupees/item

Calculating this:
- **SP** = 120 × 1.20 = 144 rupees

### Step 4: Calculate the Profit
Profit is calculated by subtracting the cost price from the selling price.

- **Profit** = Selling Price - Cost Price
- **Profit** = 144 - 129.6 = 14.4 rupees

### Step 5: Calculate the Profit Percentage
Profit percentage is calculated using the formula:

\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]

Substituting the values:
- Profit = 14.4 rupees
- Cost Price = 129.6 rupees

Calculating the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{14.4}{129.6} \right) \times 100 \]

To simplify:
- Dividing both the numerator and denominator by 14.4:
\[ \text{Profit Percentage} = \left( \frac{1}{9} \right) \times 100 \approx 11.11\% \]

Rounding to one decimal place, we get:
- **Profit Percentage** = 11.1%

### Final Answer
The gain percent is **11.1%**.

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