A shopkeeper sells a table at a discount of 20% and earns a profit of 60%. If he sells the same table at 40% discount, then what will be his new profit per cent ?

Options

A. 20
B. 30
C. 35
D. 40

Answer

To solve the problem step by step, we need to determine the cost price (CP) and the selling price (SP) of the table when the shopkeeper sells it at different discounts.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- The shopkeeper sells the table at a 20% discount and earns a profit of 60%.
- We need to find out the new profit percentage when the discount is increased to 40%.

2. **Let’s Assume the Cost Price (CP):**
- Let the cost price (CP) of the table be \( x \).

3. **Calculate the Selling Price (SP) at 20% Discount:**
- If the profit is 60%, then the selling price (SP) can be calculated as:
\[ SP = CP + Profit = x + 0.6x = 1.6x \]
- The selling price is also related to the marked price (MP) after applying the discount:
\[ SP = MP - (20\% \text{ of } MP) = MP \times (1 - 0.2) = 0.8 \times MP \]

4. **Equating the Two Expressions for SP:**
- We can set the two expressions for SP equal to each other:
\[ 1.6x = 0.8 \times MP \]
- Rearranging gives us:
\[ MP = \frac{1.6x}{0.8} = 2x \]

5. **Calculate the Selling Price (SP) at 40% Discount:**
- Now, if the shopkeeper sells the table at a 40% discount, the new selling price (SP) will be:
\[ SP = MP - (40\% \text{ of } MP) = MP \times (1 - 0.4) = 0.6 \times MP \]
- Substituting the value of MP:
\[ SP = 0.6 \times (2x) = 1.2x \]

6. **Calculate the New Profit:**
- The new profit can be calculated as:
\[ \text{Profit} = SP - CP = 1.2x - x = 0.2x \]

7. **Calculate the New Profit Percentage:**
- The profit percentage is given by:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{0.2x}{x}\right) \times 100 = 20\% \]

### Final Answer:
The new profit percentage when the table is sold at a 40% discount is **20%**.