Rajnish buys 30 books and 65 pens. If the price of each book is more than the price of each pen, what is the total amount he has to pay?

Given statements:

A. He sells all the items at a 20% profit for Rs 3828.

B. The cost price of one book and one pen together is Rs 90.

C. The difference between the sum and the difference of the cost prices of one pen and one book is Rs 28.

Which of the following statements or combinations of statements are sufficient to find the total amount Rajnish has to pay?

Question

Rajnish buys 30 books and 65 pens. If the price of each book is more than the price of each pen, what is the total amount he has to pay?

Given statements:

A. He sells all the items at a 20% profit for Rs 3828.

B. The cost price of one book and one pen together is Rs 90.

C. The difference between the sum and the difference of the cost prices of one pen and one book is Rs 28.

Which of the following statements or combinations of statements are sufficient to find the total amount Rajnish has to pay?

Accepted Answer

**Solution:**

1. From statement A:
   - Rajnish sells all items at a 20% profit for Rs 3828.
   - Let the total cost price be *CP*.
   - Since selling price (SP) = CP + 20% of CP = 1.2 × CP,
   - So, $3828 = 1.2 	imes CP \Rightarrow CP = \frac{3828 	imes 100}{120} = 3190$.

2. From statements B and C:
   - Let the cost price of one book be *x* and one pen be *y*.
   - From B: $x + y = 90$.
   - From C: The difference between sum and difference of *x* and *y* is 28.
     That is, $(x + y) - (x - y) = 28 \Rightarrow 2y = 28 \Rightarrow y = 14$.
   - Substitute $y=14$ in $x + y = 90$ gives $x = 76$.

3. Calculate total cost price:
   - Total cost = $30 	imes 76 + 65 	imes 14 = 2280 + 910 = 3190$.

4. Both methods give the same total cost price.

**Answer:** B and C together are sufficient to find the total amount Rajnish has to pay.

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