Question

(ii) A businessman bought some items for rs 2000. He kept 10 items for himself and
sold the remaining at a profit of rs 25 per item. From the amount he received in this
deal, he could buy 15 more items. Find the original price of each item.​

Answer 1

Answer:

please mark this answer as brain list

Answer 2

Given,

The cost of the items bought by the businessman = ₹ 2000

The number of items he kept for himself = 10

The profit he earned per each item he sold = ₹ 25

The number of items he could buy with the profit = 15

To find,

Calculating the original price of each item.

Solution,

We can solve the given problem by using the following process.

Let the original price of each item =  $x$

The total number of items bought using ₹ 2000 $= \frac{2000}{x}$

The number of items sold $=\frac{2000}{x} - 10$

The selling price of each item $=x+25$

Now,

                       $(\frac{2000}{x} -10)(x+25) = 2000+15x\\\\\frac{2000-10x}{x}(x+25) =2000+15x\\\\(2000-10x)(x+25)=(2000+15x)x\\\\5(400-2x)(x+25)=5(400+3x)x\\\\(400-2x)(x+25)=400x+3x^{2} \\\\400x+10000-2x^{2} -50x=400x+3x^{2} \\\\5x^{2} +50x-10000=0\\\\x^{2} +10x-2000=0$

The formula to find the roots of a quadratic equation is as follows,

                     $x^{2} +50x-40x-2000=0\\\\x(x+50)-40(x+50)\\\\(x+50)(x-40)=0\\\\x=40,x=-50$

                            $x\neq -50$

Hence, the original cost of each item = ₹ 40