Question : An article is marked 25% above its cost price. If $x$% discount is allowed on the marked price and still there is a profit of 5.5%, then what is the value of $x$?
Option 1: 16.4
Option 2: 15.4
Option 3: 13.6
Option 4: 15.6
Correct Answer: 15.6
Solution :
Given,
An article is Marked 25% above the cost price.
After giving $x$% discount still makes a profit of 5.5%.
We know,
SP = [$\frac{100 + \text{gain percentage}}{100}$] × CP
And, SP = [MP – (MP × discount percentage)]
Let the cost price of the article be 100 units.
According to the question,
The selling price of the article is
= $[\frac{100 + 5.5}{100}] × 100$
= 105.5 units
The Marked price of the article is
= [100 + (100 × 25%)]
= 100 + 25
= 125 units
Also,
The selling price of the article is = 105.5
⇒ [125 – (125 × $x$%)] = 105.5
⇒ 125 – $\frac{5x}{4}$ = 105.5
⇒ $\frac{5x}{4}$ = 19.5
⇒ $x = \frac{19.5 × 4}{5}$
⇒ $x = 15.6$
Hence, the correct answer is 15.6.
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