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Home » A man buys a number of 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?
A man buys a number of 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?
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
A man buys a number of 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?

Let the total number of pens be x.

According to the question:

\begin{array}{l} \frac{80}{x}-\frac{80}{x+4}=1 \\ \Rightarrow \frac{80(x+4)-80 x}{x(x+4)}=1 \\ \Rightarrow \frac{80+320-80 x}{x^{2}+4 x}=1 \\ \Rightarrow 320=x^{2}+4 x \\ \Rightarrow x^{2}+4 x-320=0 \\ \Rightarrow x^{2}+(20-16) x-320=0 \\ \Rightarrow x^{2}+20 x-16 x-320=0 \\ \Rightarrow x(x+20)-16(x+20)=0 \\ \Rightarrow(x+20)(x-16)=0 \\ \Rightarrow x=-20 \text { or } x=16 \end{array}

The total number of pens cannot be negative; therefore, the total number of pens is 16 .

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