Question

A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less. How many pens did he buy?

Answer 1

Given: A man buys a number of pens for ₹ 180. If he had bought 3 more pens for the same amount, each pen would have cost him ₹ 3 less.

Step-wise calculation:

1. Let the original number of pens = x.

2. Original cost per pen = `180/x`.

3. If he bought 3 more pens, number = x + 3 and new cost per pen = `180/(x + 3)`.

4. According to the question: 

`180/x - 180/(x + 3) = 3`

5. Simplify:

`(180(x + 3) - x)/(x(x + 3)) = 3`

⇒ `(180 xx 3)/(x(x + 3)] = 3`

6. Divide both sides by 3:

`180/(x(x + 3)) = 1`

⇒ x(x + 3) = 180

7. So, x² + 3x – 180 = 0

⇒ (x + 15)(x – 12) = 0

8. x > 0

⇒ x = 12

He bought 12 pens.