A tailor had a piece of cloth. He initially reduced its length by 80%. After this, he further shortened it by 90% of its new length. What was the percentage decrease in the cloth's length from the first to the second cut?
- 50%
- 80%
- 30%
- 40%
The Correct Option is A
Solution and Explanation
Let's assume the initial length of the cloth is 100 units.
After the first cut, the length becomes: 100 - (80% of 100) = 100 - 80 = 20 units.
After the second cut, the length becomes: 20 - (90% of 20) = 20 - 18 = 2 units.
The decrease from the point after the first cut (20 units) to the point after the second cut (2 units) is 20 - 2 = 18 units.
To find the percentage decrease, we divide the decrease by the original value after the first cut and multiply by 100:
Percentage decrease =\(\left( \frac{18}{20} \right) \times 100 = 90\%\)
Since the value after the first cut is 20 units and it decreased to 2 units, which is half of 20 units, the percentage decrease is 50%.
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