Question

a person bought a certain number of pens for 800 rupees . if he had bought 4 pens more for the same money, he would have paid rs10 less for each pen. how many pens did he buy? ​

Answer 1

Answer:80 pens

Step-by-step explanation:

Let person buy x number of pens

So. One pen costs 800/x

If he buy 4 more pens means (x+4) pens then one pen will cost

(800/x-10).

So total rupees to buy x+4 pens

(x+4)*(800/x-10)

=800+3200/x-10x-40

Multiplying above by x,

-10x^2+760x+3200

Solving, we get

x=-4 and x=80

As -4 is not acceptable

80 pens are bought by the person

Answer 2

The number of pens is 16.

Given:

The total cost of pens = 800 rupees

To Find:

The number of pens

Solution:

Let X be the number of pens.

By given condition

$\frac{\ 800}{X}-\frac{800}{X+4} = 10\\\ \frac{800(X+4)-800X}{X(X+4)} =10\\\\\frac{800X+3200-800X}{X^{2}+4X } =10\\\\\frac{3200}{X^{2} +4X} = 10\\\\3200 = 10X^{2} +40X\\\\10X^{2}+40X -3200=0\\\\X^{2}+4X-320 =0$

Here a= 1, b=4 and c= -320

Case 1)

$X = \frac{-4+\sqrt{16+4*1320} }{2} \\\\ X = \frac{-4+36}{2} \\\\X= \frac{32}{2} \\\\X=16$

Case 2)

$X = \frac{-4-\sqrt{16+4*1320} }{2} \\\\ X = \frac{-4-36}{2} \\\\X= \frac{-40}{2} \\\\X=-20$

X cannot be a negative value.

∴ X=16.

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