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

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answer is B.

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Detailed Solution

Given that total price of the pen = Rs.180.
Let’s assume that the number of pens is

p

and the price per pen is Rs

q

.
Then,
Number of pens bought

\times

price per pen = total price of the pens

⟹

p \times q = 180

⟹ q = \frac{180}{p}

… (1)
According to the given condition,
If man bought 3 more pens for the same amount, but the price gets reduced by Rs.3. Then,

⟹ (p + 3) (q - 3) = 180

⟹ (p + 3) (\frac{180}{p} - 3) = 180

⟹ p (\frac{180}{p} - 3) + 3 (\frac{180}{p} - 3) = 180

⟹ (180 - 3 p) + \frac{540}{p} - 9 = 180

⟹ 180 p - 3 p^{2} + 540 - 9 p = 180 p

⟹ 3 p^{2} + 9 p - 540 = 0

⟹ p^{2} + 3 p - 180 = 0

⟹ p^{2} + 15 p - 12 p - 180 = 0

⟹ p (p + 15) - 12 (p + 15) = 0

⟹ (p + 15) (p - 12) = 0

⟹ p + 15 = 0 or p - 12 = 0

∴ p = - 15 or p = 12

∴ Man bought a total of 12 pens.
Hence, the correct option is 2.

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