Question

A businessman bought some items for `3000. He kept 10 items for

himself and sold the remaining at a profit of `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

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$\large \tt \red{✦Answer✦}$

Given :- A businessman bought some items for 3000. He kept 10 items for himself and sold the remaining at a profit of 25 per item. From the amount he received in this deal, he could buy 15 more items. Find the original price of each item. ?

Solution :-

Let us assume that, the businessman buy total x items .

now,

→ Total CP of x items = Rs. 3000

then,

→ CP of each item = Rs.(3000/x)

Now, he kept 10 items for himself sold the remaining at a profit of 25 per item .

So,

→ items left = (x - 10)

→ Profit on each item = Rs.25

then,

→ SP = CP + Profit

→ Total SP = (x - 10) * [(3000/x) + 25)] = Rs. (x-10)[(3000 + 25x)/x]

Now, given that, he could buy 15 more items from this profit.

then we can conclude that, he can buy total (x + 15) items from given SP .

therefore,

→ (x - 10)[(3000 + 25x)/x] = (3000/x) * (x + 15)

→ (x - 10)(3000 + 25x) = (3000) * (x + 15)

→ 3000x + 25x² - 30000 - 250x = 3000x + 45000

→ 25x² - 250x - 30000 - 45000 = 0

→ 25x² - 250x - 75000 = 0

→ x² - 10x - 3000 = 0

→ x² - 60x + 50x - 3000 = 0

→ x(x - 60) + 50(x - 60) = 0

→ (x - 60)(x + 50) = 0

→ x = 60 or (-50) .

since items cant be in negative..

hence,

→ Total items he bought = 60 .

∴

→ The original price of each item = 3000/60 = Rs.50 (Ans.)

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Answer 2

Answer:

75 is the price of each article

Step-by-step explanation:

let the no of items be x so

for x items he gave 3000

on each=3000/x

he kept 10

so x-10 items

one item would be of 3000/x-10

profit of 25 per item so

(3000/x-10)-(3000/x)=25

3000[(1/x-10)-1/x]=25

3000[x-x+10/x²-10x]=25

3000[10/x²-10x]=25

cut 3000 by 25 so

120×10=x²-10x

x²-10x=1200

x²-10x-1200=0

x²-40x+30x-1200=0

x(x-40)+30(x-40)=0

(x+30)(x-40)=0

x can't be -30 coz items cannot be in negative no

so x=40

items were 40

one item price =3000/40

=75

If you have not understood please do comment

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