Q) By selling an article for Rs. 48, a trader loses as much percent as half of the cost price of the article. Calculate the cost price and loss amount of the article.

(Q 32 – 30/5/2 – CBSE 2026 Question Paper)

Ans:

Let’s consider the cost price of the article is Rs. x

∴ Half of the cost price =

By given condition, Loss = “as much percent as half of the cost price”

∴ Loss = %

∵ Sale price is 48

∴ loss of sale price of Rs. 48 = Cost price – Sale price = x – 48

∴ % loss = x 100

∴ x 100 =  

∴ 200 (x – 48) = x ²

∴ x ² – 200 x + 9600 = 0

∴ x ² – 200 x + 9600 = 0

∴ x ² – 120 x – 80 x + 9600 = 0

∴ x (x – 120) – 80 (x – 120) = 0

∴ (x – 120)(x – 80) = 0

∴ x = 120 and x = 80

Therefore, the Cost Price is either Rs. 120 (with a loss of Rs. 72) or Rs. 80 (with a loss of Rs. 32).

Check:
For x = 120, & SP = 48, Loss = 48 – 120 = – 72, and loss % = x 100 = 60%, which is half of 120.
For x = 80, & SP = 48, Loss = 48 – 80 = – 32, and loss % = x 100 = 40%, which is half of 80.
Since given condition is met for both the values, our solution is correct.

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