The marked price of an article is 40\% above its cost price. When the shopkeeper offers a discount of $d$% on the marked price, he earns a profit of ______\% and when the discount is doubled to $2d$\%, he earns a profit of ______\%. Which of the following pairs of profit percentages correctly fill the blanks?

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**Solution:**

1. Let the cost price (CP) of the article be $100x$ Rs.
2. Then the marked price (MP) is 40\% above CP, so:
   $$MP = 100x + 40\% \times 100x = 140x \text{ Rs.}$$

3. For each option, we check if the given profit percentages correspond to a valid discount $d$% and its double $2d$%:

- **Option (A): (22.5\%, 5\%)**
  - Profit at discount $d$% is 22.5\%, so selling price (SP) = $122.5x$ Rs.
  - Discount $d$% = $\frac{140x - 122.5x}{140x} \times 100 = 12.5\%$
  - When discount is doubled ($2d = 25\%$), SP = $140x \times 0.75 = 105x$ Rs.
  - Profit = $105x - 100x = 5x$, profit percentage = $\frac{5x}{100x} \times 100 = 5\%$
  - Both profit values match, so option (A) is valid.

- **Option (B): (33\%, 26\%)**
  - Profit at discount $d$% is 33\%, so SP = $133x$ Rs.
  - Discount $d$% = $\frac{140x - 133x}{140x} \times 100 = 5\%$
  - When discount is doubled ($2d = 10\%$), SP = $140x \times 0.90 = 126x$ Rs.
  - Profit = $126x - 100x = 26x$, profit percentage = 26\%
  - Both profit values match, so option (B) is valid.

- **Option (C): (19\%, 2\%)**
  - Profit at discount $d$% is 19\%, so SP = $119x$ Rs.
  - Discount $d$% = $\frac{140x - 119x}{140x} \times 100 = 15\%$
  - When discount is doubled ($2d = 30\%$), SP = $140x \times 0.70 = 98x$ Rs.
  - Profit = $98x - 100x = -2x$, which is a loss, not a profit.
  - Hence, option (C) is invalid.

- **Option (D): (26\%, 12\%)**
  - Profit at discount $d$% is 26\%, so SP = $126x$ Rs.
  - Discount $d$% = $\frac{140x - 126x}{140x} \times 100 = 10\%$
  - When discount is doubled ($2d = 20\%$), SP = $140x \times 0.80 = 112x$ Rs.
  - Profit = $112x - 100x = 12x$, profit percentage = 12\%
  - Both profit values match, so option (D) is valid.

- **Option (E): (23.2\%, 6.4\%)**
  - Profit at discount $d$% is 23.2\%, so SP = $123.2x$ Rs.
  - Discount $d$% = $\frac{140x - 123.2x}{140x} \times 100 = 12\%$
  - When discount is doubled ($2d = 24\%$), SP = $140x \times 0.76 = 106.4x$ Rs.
  - Profit = $106.4x - 100x = 6.4x$, profit percentage = 6.4\%
  - Both profit values match, so option (E) is valid.

**Conclusion:** Options (A), (B), (D), and (E) satisfy the conditions, while (C) does not.

**Answer:** Only options (A), (B), (D), and (E) are possible to fill both blanks.

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