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Question
A cloth merchant advertises selling cloth at a 4% loss. By using a faulty meter scale, he is earning a profit of 20%. What is the actual length of the scale?
Solution
Let the cost price of the cloth be ₹ ‘x’ per meter
He claims a loss of 4%
∴ The selling price of the cloth
S.P. = C.P.`(1 - "loss%"/100)`
= `"x"(1 - 4/100)`
= 0.96x ..............(i)
The actual cost price of the cloth is lower as the cloth is measured by a faulty meter scale.
Given that shopkeeper’s profit = 20%
Now, S.P. = C.P.`(1 + "Profit%"/100)`
∴ S.P. = C.P. ÷ `(1 + "Profit%"/100)`
∴ Actual C.P. = 0.96x ÷ `(1 + 20/100)` ......[From (i)]
= `0.96"x" ÷ (1 + 1/5)`
= 0.96x ÷ `6/5`
= 0.96x × `5/6`
= 0.8x
∴ The actual cost price is 0.8 times the cost price as advertised. In other words, the meter scale used for the fraud is 0.8 times the meter scale that should have been used.
∴ The length of the faulty meter scale used
= 0.8 × 1
= 0.8 meter
∴ The actual length of the scale is 0.8 meters.
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