A man allows a discount of 10% on a book whose marked price is Rs.40. What is the cost price so that the profit is 20% ?

Options

A. Rs 35
B. Rs 40
C. Rs 30
D. Rs 45

Answer

To find the cost price of the book such that the profit is 20% after allowing a discount of 10% on the marked price of Rs. 40, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price of the book is Rs. 40, and a discount of 10% is given.

**Calculation:**
- Discount = 10% of Rs. 40
- Discount = (10/100) * 40 = Rs. 4

Now, we subtract the discount from the marked price to find the selling price (SP).

- Selling Price (SP) = Marked Price - Discount
- SP = 40 - 4 = Rs. 36

### Step 2: Set Up the Equation for Cost Price
Let the cost price (CP) of the book be Rs. Y. We want to find Y such that the profit is 20%.

**Profit Calculation:**
- Profit = Selling Price - Cost Price
- We know that Profit = 20% of Cost Price
- Therefore, Profit = (20/100) * Y = 0.2Y

### Step 3: Write the Profit Equation
From the above, we can write the equation:

- Selling Price = Cost Price + Profit
- 36 = Y + 0.2Y

### Step 4: Simplify the Equation
Combine like terms:

- 36 = Y + 0.2Y
- 36 = 1.2Y

### Step 5: Solve for Cost Price
Now, we can solve for Y:

- Y = 36 / 1.2
- Y = 30

### Conclusion
The cost price of the book should be Rs. 30 to achieve a profit of 20% after allowing a 10% discount on the marked price.