SOLUTION: A man bought some chairs for Rs 200/- .Five chairs were stolen from the total. He sold the remaining chairs for a profit of Rs 40 The selling price of chair was Rs 4 more than its

Algebra ->  Equations -> SOLUTION: A man bought some chairs for Rs 200/- .Five chairs were stolen from the total. He sold the remaining chairs for a profit of Rs 40 The selling price of chair was Rs 4 more than its       Log On


   

Question 191320: A man bought some chairs for Rs 200/- .Five chairs were stolen from the total. He sold the remaining chairs for a profit of Rs 40 The selling price of chair was Rs 4 more than its cost price. How many chairs did he buy and how much was the cost price of each chair?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A man bought some chairs for Rs 200/- .Five chairs were stolen from the total.
He sold the remaining chairs for a profit of Rs 40.
The selling price of chair was Rs 4 more than its cost price.
How many chairs did he buy and how much was the cost price of each chair?
:
Let x = no. of chairs bought originally
then
200%2Fx = cost of each chair he bought
:
(x-5) = no. of chairs sold
;
Since he made $40 profit, selling price must be: 240%2F%28x-5%29
:
Selling price - unit cost = 4
240%2F%28x-5%29 - 200%2Fx = 4
Multiply equation by x(x-5), results:
240x - 200(x-5) = 4x(x-5)
;
240x - 200x + 1000 = 4x^2 - 20x
:
40x + 1000 = 4x^2 - 20x
:
0 = 4x^2 - 20x - 40x - 1000
A quadratic equation:
4x^2 - 60x - 1000 = 0
Simplify, divide by 4
x^2 - 15x - 250 = 0
Factor
(x-25)(x+10) = 0
The positive solution
x = 25 chairs originally purchased
;
Find original cost:
200%2F25 = $8 per chair
:
Selling price (5 fewer chairs sold):
240%2F20 = $12 per chair (which is a $4 profit on ea chair)