**What is the profit percent earned on selling 2 books and 1 pen?**

Given the following statements:

**A.** Cost price of 3 books is equal to the selling price of 4 pens. Profit earned on selling 2 pens is equal to the profit earned on selling 1 book. Profit earned on selling 4 pens is 50\% of their cost price.

**B.** Profit earned on selling 2 books and 6 pens is 50\%, which is equal to 500\% of the cost price of one pen.

**C.** Profit earned on selling one book is 100\% of the cost price of one pen.

**Which of the following options is correct?**

Question

**What is the profit percent earned on selling 2 books and 1 pen?**

Given the following statements:

**A.** Cost price of 3 books is equal to the selling price of 4 pens. Profit earned on selling 2 pens is equal to the profit earned on selling 1 book. Profit earned on selling 4 pens is 50\% of their cost price.

**B.** Profit earned on selling 2 books and 6 pens is 50\%, which is equal to 500\% of the cost price of one pen.

**C.** Profit earned on selling one book is 100\% of the cost price of one pen.

**Which of the following options is correct?**

Accepted Answer

**Solution:**

1. **From statement A:**
   - Let the selling price (SP) of 4 pens be $12x$.
   - Given, cost price (CP) of 3 books = SP of 4 pens = $12x$.
   - Profit on selling 4 pens is 50\% of their CP.
     - Therefore, CP of 4 pens = $\frac{12x 	imes 100}{150} = 8x$.
     - Profit on 4 pens = SP - CP = $12x - 8x = 4x$.
   - Profit on selling 2 pens = $\frac{4x}{2} = 2x$.
   - Profit on selling 1 pen = $x$.
   - Profit on selling 1 book = profit on 2 pens = $2x$.
   - Profit on selling 2 books = $2 	imes 2x = 4x$.
   - Total profit on selling 2 books and 1 pen = $4x + x = 5x$.
   - Total cost price of 2 books and 1 pen = CP of 3 books + CP of 1 pen - but since CP of 3 books = $12x$ and CP of 4 pens = $8x$, CP of 1 pen = $\frac{8x}{4} = 2x$.
   - So, CP of 2 books = $\frac{2}{3} 	imes 12x = 8x$.
   - CP of 1 pen = $2x$.
   - Total CP = $8x + 2x = 10x$.
   - Profit percentage = $\frac{	ext{Profit}}{	ext{CP}} 	imes 100 = \frac{5x}{10x} 	imes 100 = 50\%$.

Hence, statement A alone is sufficient to find the profit percent.

2. **From statement B:**
   - Profit on selling 2 books and 6 pens is 50\%, which equals 500\% of the CP of one pen.
   - Let SP of 2 books = $12x$, SP of 6 pens = $18y$.
   - Total profit = $\frac{50}{100} 	imes (12x + 18y) = 6x + 9y$.
   - This profit equals 500\% of CP of one pen, but CP of pen is unknown.
   - Without CP of pen, we cannot find profit percent on 2 books and 1 pen.

So, statement B alone is insufficient.

3. **From statement C:**
   - Profit on one book = 100\% of CP of one pen.
   - Let CP of pen = $a$, CP of book = $b$.
   - SP of book = $b + a$.
   - No information about CP or SP of pens or books individually, so cannot calculate profit percent.

4. **Combining B and C:**
   - Still insufficient to find exact profit percent due to multiple unknowns.

**Conclusion:** Only statement A alone provides enough information to calculate the profit percent on selling 2 books and 1 pen.

**Answer:** (e) Only statement A is sufficient to answer.

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