A cloth was 50cm broad and 8 cm long. When washed, it was found to have lost 25% of its length and 14% of its breath. Then the percentage decreased in area is ..........

Options

A. `34.5%`
B. ` 35.5% `
C. ` 36% `
D. `35%`

Answer

To solve the problem of finding the percentage decrease in the area of the cloth after washing, we can follow these steps:

### Step 1: Calculate the initial dimensions of the cloth.
- **Initial breadth (B)** = 50 cm
- **Initial length (L)** = 8 cm

### Step 2: Calculate the initial area of the cloth.
- **Initial Area (A_initial)** = Length × Breadth = 8 cm × 50 cm = 400 cm²

### Step 3: Calculate the new dimensions after washing.
- The cloth loses 25% of its length:
- New length = Initial length - (25% of Initial length)
- New length = 8 cm - (0.25 × 8 cm) = 8 cm - 2 cm = 6 cm

- The cloth loses 14% of its breadth:
- New breadth = Initial breadth - (14% of Initial breadth)
- New breadth = 50 cm - (0.14 × 50 cm) = 50 cm - 7 cm = 43 cm

### Step 4: Calculate the new area of the cloth.
- **New Area (A_final)** = New Length × New Breadth = 6 cm × 43 cm = 258 cm²

### Step 5: Calculate the decrease in area.
- Decrease in area = Initial Area - New Area
- Decrease in area = 400 cm² - 258 cm² = 142 cm²

### Step 6: Calculate the percentage decrease in area.
- Percentage decrease in area = (Decrease in area / Initial Area) × 100%
- Percentage decrease in area = (142 cm² / 400 cm²) × 100% = 35.5%

### Final Answer:
The percentage decrease in area is **35.5%**.

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