The sale price of an article is 25% more than its cost price. If the s

Solution

Step 1: Understand Question Statement

• The sale price of an article is 25% more than its cost price.
• The sale price is an integer.

Step 2: Define Methodology

• Let us assume the sale price and cost price of the article (in dollars) as SP and CP, respectively.

o \(SP = CP + CP*\frac{25}{100}\)\( = CP*(1+\frac{25}{100}) =CP*\frac{125}{100} =CP*\frac{5}{4}\)
• Since, SP is an integer, so \(CP*\frac{5}{4}\) must be an integer.

o This means, CP must be a multiple of 4.

Step 3: Calculate the final answer

• Option A: $60

o \(\frac{60}{4} =15\); So, it is a multiple of 4.
• Option B: $80

o \(\frac{80}{4} =20\); So, it is a multiple of 4.
• Option C: $100

o \(\frac{100}{4} =25\); So, it is a multiple of 4.
• Option D: $150

o \(\frac{150}{4} =\frac{75}{2 }\)which is not an integer. So, clearly 150 is not a multiple of 4.
• Option E: $200

o \(\frac{200}{4} =50\); So, it is a multiple of 4.