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An article is sold at a certain price. By selling it at 5/7th of that price on loss 20%. Find the gain percentage at the original sold price.
Question

An article is sold at a certain price. By selling it at 5/7th of that price on loss 20%. Find the gain percentage at the original sold price.

A.

20%        

B.

12%

C.

15.6%

D.

18%

Correct option is B

Given:
Let the original selling price be 'x'
New selling price = (5/7)x
Loss on new selling price = 20%

Formula Used:
Gain percentage=(GainCP)×100\text{Gain percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100

​Solution:
​If selling at (5/7)x results in a 20% loss, it means:​​
57x=0.8×Cost Price\frac{5}{7}x = 0.8 \times \text{Cost Price}​​
Cost Price=2528x\text{Cost Price} = \frac{25}{28}x
Gain = Original Selling Price - Cost Price
Gain=x2528x=328x\text{Gain} = x - \frac{25}{28}x = \frac{3}{28}x​​​
Gain percentage=(GainCP)×100\text{Gain percentage} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100​​
Gain Percentage=(328x2528x)×100\text{Gain Percentage} = \left( \frac{\frac{3}{28}x}{\frac{25}{28}x} \right) \times 100​​
Gain Percentage=(325)×100=12%\text{Gain Percentage} = \left( \frac{3}{25} \right) \times 100 = 12\%​​
Hence, the gain percentage at the original selling price is 12%.

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