Question

Vidya bought some pens for Rs75 had she bought 10 more pens for the same amount each pen would have cost her Rs2 less find the number of pens bought by Vidya

Answer 1

Vidya brought 15 pens

Answer 2

Answer:

Vidya bought 15 pens.

Step-by-step explanation:

Let x be the no of pen Vidya bought in start.

So, Cost of x pens = 75

     Cost of 1 pen =  $\frac{75}{x}$

Now she buy 10 more pens.

⇒ Cost of ( x + 10 ) pens = 75

   Cost of 1 pen =  $\frac{75}{x+10}$

According to Question, this purchase cost her Rs. 2 less for each pen

Thus,

$\frac{75}{x}-\frac{75}{x+10}=2$

$\frac{75(x+10)-75x}{x(x+10)}=2$

$\frac{75x+750)-75x}{x^2+10x}=2$

$750=2\times(x^2+10x)$

$x^2+10x=\frca{750}{2}$

x² + 10x = 375

x² + 10x - 375 = 0

x² + 25x - 15x - 375 = 0

x ( x + 25 ) - 15 ( x + 25 ) = 0

( x + 25 ) ( x - 15 ) = 0

⇒ x + 25 = 0         and         x - 15 = 0

   x = -25               and         x = 15      

No of pens can not be negative.

⇒ x = 15 is taken.

Therefore, Vidya bought 15 pens.