Question

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?

Answer 1

Let the number of pens bought initially be x

Total cost = Rs 180

Cost of each pen = Rs $\left(\frac{180}{x}\right)$

Number of pens increased = 3

Now total number of pens = $(x+3)$

New cost of each pen = Rs $\frac{180}{(x+3)}$

By the given problem, we have

$\frac{180}{x}-\frac{180}{x+3}=3$

$180(x+3-x)=3\left(x\right)(x+3)$

$180=x^2+3x$

$x^2+3x-180=0$

$x^2+(15-12)x-180=0$

$x^2+15x-12x-180=0$

$x(x+15)-12(x+15)=0$

⇒$(x+15)(x–12)=0$

$\therefore x=-15orx=12$

Since x cannot be negative, x = 12
Hence the number of pens bought initially is 12