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Question:

An article is marked x% above the cost price. A discount of 2/3x% if given on the marked price. If the profit is 4% of the cost price and the value of x lies between 25 and 50, then the value of 50% of x is:

Explanation:

Let the CP of the article be Rs 100. 

∴ M.P = 100 + x

As a discount of 2x/3 % is given on the Marked Price. 
 
SP = (100 + x)$\left(1-\frac{2x/3}{100}\right)$   …(1)

Also, since profit is 4%, it means selling price = 100 + 4 = 104   …(2)
 
Equating (1) and (2)

⇒ (100 + x)$\left(1-\frac{2x/3}{100}\right)$ = 104

⇒ 100 + x – $\frac{2x}{3}$ – $\frac{2x^2}{300}$ = 104

⇒ $\frac{2x^2}{300}$ - $\frac{x}{3}$ + 4 = 0

⇒ x² – 50x + 600 = 0

⇒ x = 20 or 30.

Since it is given that x is between 25 and 50 hence x = 30.

∴ 50% of 30 = 15.

Hence, option (a).