Adda 247 publication sold a puzzle book in Rs. 475 and made profit of `25%` on CP and sold a DI book in Rs. 575 and made a profit of `15%` on CP. If publication sold puzzle book in Rs. 360, then find what price should Di book will be sold to made a profit of `30%`on both books?

Options

A. A)Rs. 784
B. B)Rs.874
C. C)Rs. 847
D. D)Rs. 748

Answer

To solve the problem step by step, we will first determine the cost prices (CP) of both the puzzle book and the DI book based on the selling prices (SP) and the profit percentages given. Then, we will calculate the selling price required for the DI book to achieve an overall profit of 30%.

### Step 1: Calculate the Cost Price of the Puzzle Book

Given:
- Selling Price of the Puzzle Book (SP) = Rs. 475
- Profit Percentage = 25%

To find the Cost Price (CP), we use the formula:
\[ CP = \frac{SP}{1 + \frac{Profit\%}{100}} \]
Substituting the values:
\[ CP_{puzzle} = \frac{475}{1 + 0.25} = \frac{475}{1.25} = 380 \]

### Step 2: Calculate the Cost Price of the DI Book

Given:
- Selling Price of the DI Book (SP) = Rs. 575
- Profit Percentage = 15%

Using the same formula:
\[ CP_{DI} = \frac{575}{1 + \frac{Profit\%}{100}} = \frac{575}{1 + 0.15} = \frac{575}{1.15} \approx 500 \]

### Step 3: Calculate the Overall Cost Price

Now, we need to find the overall cost price of both books:
\[ Total\ CP = CP_{puzzle} + CP_{DI} = 380 + 500 = 880 \]

### Step 4: Calculate the Total Selling Price for a 30% Profit

To achieve an overall profit of 30%, we calculate the required total selling price (SP):
\[ Required\ SP = Total\ CP \times (1 + \frac{30}{100}) = 880 \times 1.3 = 1144 \]

### Step 5: Calculate the Selling Price of the DI Book

We know that the puzzle book is sold for Rs. 360. Thus, we can set up the equation:
\[ Total\ SP = SP_{puzzle} + SP_{DI} \]
Substituting the known values:
\[ 1144 = 360 + SP_{DI} \]
Now, solving for \(SP_{DI}\):
\[ SP_{DI} = 1144 - 360 = 784 \]

### Final Answer

The selling price of the DI book to achieve a 30% profit on both books should be Rs. 784.

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