A towel was 50 cm broad and 100 cm long. When bleached it was found to have lost 20% of its length and 10% of its breadth What was the percent decrease in area?
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Answer:
The percentage decrease in area = 28%
Step-by-step explanation:
Given:
- A towel was 50 cm broad and 100 cm long.
- When bleached it was found to have lost 20% of its length and 10% of its breadth.
To find:
- What was the percent decrease in area?
Solution:
- Length of a towel = 100 cm
- Breadth of a towel = 50 cm
♦ Area of a towel = l × b
Where,
l is the length of a towel.
b is the breadth of a towel.
- Area of a towel = 100 × 50
- Area of a towel = 5000 cm²
When bleached it was found to have lost 20% of its length and 10% of its breadth.
- New Length = 100 - 20/100 × 100
- New Length = 100 - 20
- New Length = 80 cm
- New Breadth = 50 - 10/100 × 50
- New Breadth = 50 - 10/10 × 5
- New Breadth = 50 - 10/2
- New Breadth = 50 - 5
- New Breadth = 45 cm
- New Area of towel = l × b
- New Area of towel = 80 × 45
- New Area of towel = 3600 cm²
Now,
- Decrease in area = Area of a towel before - New Area of towel ( after )
- Decrease in area = 5000 - 3600
- Decrease in area = 1400 cm²
Finally,
- Percentage decrease in area = 1400/5000 × 100%
- Percentage decrease in area = 14/50 × 100%
- Percentage decrease in area = 14/5 × 10%
- Percentage decrease in area = 14 × 2%
- Percentage decrease in area = 28%
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