Marked price of an article is 60% more than the CP of the article. When it is solid at x% discount then _______% percent profit is obtained and when it is sold at a discount of 2x%, _______% profit is obtained.Which of the following options are possible for the blanks in sameA. 60, 30B. 20, 8C. 48, 24D. 36, 12E. 44, 28A and EB, D and EC, D and EAll are possibleA, D and E

The question asks for the possible values for the blanks in the statement. Let's solve it step by step.

Let's assume the cost price (CP) of the article is $100.

According to the given information, the marked price of the article is 60% more than the CP. So, the marked price would be $100 + 60$100 = $100 +$60 = $160.

Now, when the article is sold at x% discount, the selling price (SP) would be (100 - x)% of the marked price. So, the selling price would be (100 - x)% of $160.

Profit is calculated as SP - CP. So, the profit percentage would be ((SP - CP) / CP) * 100.

Let's calculate the profit percentage when the article is sold at x% discount:

Profit percentage = ((SP - CP) / CP) * 100 = ((100 - x)% of $160 -$100) / $100 * 100 = ((100 - x)/100 *$160 - $100) /$100 * 100 = ((100 - x)/100 * $160 -$100) * 100 / $100 = ((100 - x)/100 *$160 - $100)

Now, let's calculate the profit percentage when the article is sold at a discount of 2x%:

Profit percentage = ((SP - CP) / CP) * 100 = ((100 - 2x)% of $160 -$100) / $100 * 100 = ((100 - 2x)/100 *$160 - $100) /$100 * 100 = ((100 - 2x)/100 * $160 -$100) * 100 / $100 = ((100 - 2x)/100 *$160 - $100)

Now, we need to find the possible values for the blanks in the statement.

Let's substitute the values given in the options and see which ones satisfy the equations:

Option A: 60, 30 Profit percentage when sold at x% discount = ((100 - x)/100 * $160 -$100) = ((100 - 60)/100 * $160 -$100) = 40% Profit percentage when sold at a discount of 2x% = ((100 - 2x)/100 * $160 -$100) = ((100 - 2*60)/100 * $160 -$100) = -20% Option A does not satisfy the equations.

Option B: 20, 8 Profit percentage when sold at x% discount = ((100 - x)/100 * $160 -$100) = ((100 - 20)/100 * $160 -$100) = 36% Profit percentage when sold at a discount of 2x% = ((100 - 2x)/100 * $160 -$100) = ((100 - 2*20)/100 * $160 -$100) = 24% Option B satisfies the equations.

Option C: 48, 24 Profit percentage when sold at x% discount = ((100 - x)/100 * $160 -$100) = ((100 - 48)/100 * $160 -$100) = 28.8% Profit percentage when sold at a discount of 2x% = ((100 - 2x)/100 * $160 -$100) = ((100 - 2*48)/100 * $160 -$100) = 16.8% Option C does not satisfy the equations.

Option D: 36, 12 Profit percentage when sold at x% discount = ((100 - x)/100 * $160 -$100) = ((100 - 36)/100 * $160 -$100) = 48.8% Profit percentage when sold at a discount of 2x% = ((100 - 2x)/100 * $160 -$100) = ((100 - 2*36)/100 * $160 -$100) = 36.8% Option D satisfies the equations.

Option E: 44, 28 Profit percentage when sold at x% discount = ((100 - x)/100 * $160 -$100) = ((100 - 44)/100 * $160 -$100) = 38.4% Profit percentage when sold at a discount of 2x% = ((100 - 2x)/100 * $160 -$100) = ((100 - 2*44)/100 * $160 -$100) = 26.4% Option E satisfies the equations.

Therefore, the possible values for the blanks in the statement are:

A. 60, 30 (not possible) B. 20, 8 C. 48, 24 (not possible) D. 36, 12 E. 44, 28

So, the correct answer is D and E.