Question : A trader marks the sale price 25% more than the cost price and gives a 10% discount at the time of selling. The gain percentage is ____.
Option 1: $12\frac{1}{2}$%
Option 2: $12\frac{1}{3}$%
Option 3: $11\frac{1}{2}$%
Option 4: $12$%
Correct Answer: $12\frac{1}{2}$%
Solution :
The trader marks the selling price as 25% more than the cost price.
So, the marked price (MP) = CP + 0.25 × CP = 1.25 × CP ----------------(i)
Then, the trader gives a 10% discount at the time of selling.
So, the selling price (SP) = MP – 0.10 × MP
⇒ SP = 0.90 × MP
From equation (i), we get,
SP = 0.90 × 1.25 ×CP = 1.125 × CP
The gain percentage is:
$= \frac{SP - CP}{CP} \times 100 = \frac{1.125CP - CP}{CP} \times 100 = 12.5 =12\frac{1}{2}$%
Hence, the correct answer is $12\frac{1}{2}\%$.
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