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03 Jan 2024, 06:26
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A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale, in centimeters, that he uses when measuring 1 meter of cloth? (1 meter = 100 centimeters)
A. 70
B. 72
C. 75
D. 76
E. 77
A. 70
B. 72
C. 75
D. 76
E. 77
03 Jan 2024, 06:26
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Official Solution:
A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale, in centimeters, that he uses when measuring 1 meter of cloth? (1 meter = 100 centimeters)
A. 70
B. 72
C. 75
D. 76
E. 77
Let's assume that the cost of 1 centimeter of cloth is $1. Therefore, for a meter (100 centimeters), the base cost would be $100. However, the merchant claims to sell 1 meter of cloth at a 5% loss, which means he is selling it for $95 (95% of the original cost).
In reality, this $95 still incorporates a 25% gain for the merchant, which means \(1.25 * ($1 * \text{actual length in meters}) = $95\). This yields \(\text{actual length in meters} = 0.76\). So, the actual length of cloth the merchant claims to be 1 meter is, in fact, only 0.76 meters.
Answer: D
A cloth merchant professes to sell at a loss of 5%. However, the merchant falsifies the meter scale and gains 25%. What is the measure of the scale, in centimeters, that he uses when measuring 1 meter of cloth? (1 meter = 100 centimeters)
A. 70
B. 72
C. 75
D. 76
E. 77
Let's assume that the cost of 1 centimeter of cloth is $1. Therefore, for a meter (100 centimeters), the base cost would be $100. However, the merchant claims to sell 1 meter of cloth at a 5% loss, which means he is selling it for $95 (95% of the original cost).
In reality, this $95 still incorporates a 25% gain for the merchant, which means \(1.25 * ($1 * \text{actual length in meters}) = $95\). This yields \(\text{actual length in meters} = 0.76\). So, the actual length of cloth the merchant claims to be 1 meter is, in fact, only 0.76 meters.
Answer: D
16 Jan 2024, 23:33
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I feel that probably the measure of (false) scale that he is using to measure out 100 metres (in front of customers) should be greater than 100 metres. and should be 100/76 = 131 metres.
