SOLUTION: Ahmad brought a number of shares for Rs 1875.he reserved 15 of theme and sold remaining for Rs1740 making a profit of 4 per share on the cost price.how many share did he buy.

Question 1123893: Ahmad brought a number of shares for Rs 1875.he reserved 15 of theme and sold remaining for Rs1740 making a profit of 4 per share on the cost price.how many share did he buy.
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of shares bought.
let p = the price per share they were bought at.
let x-15 equal the number of shares sold.
let p+4 equal the price per share they were sold at.

he bought them for 1875.
he sold 15 less for 1740 at a profit of 4 each.

your equations are:

xp = 1875
(x-15) * (p+4) = 1740

these euations need to be solved simultaneously.

simplify the equations to get:

xp = 1875
xp + 4x - 15p - 60 = 1740

add 60 to both sides of the second equation and leave the first equation as is to get:

xp = 1875
xp + 4x - 15p = 1800

subtract the first equation from the second to get:

4x - 15p = -75

add 75 to both sides of this equation to get:

4x - 15p + 75 = 0

from the first original equation of xp = 1875, solve for p to get:

p = 1875/x

in the last equation of 4x - 15p + 75 = 0, replace p qith 1875/x to get:

4x - 15*1875/x + 75 = 0

multiply both sides of this equation by x to get:

4x^2 - 15*1875 + 75x = 0

simplify to get:

4x^2 - 28125 + 75x = 0

reorder the terms in descending order of degree to get:

4x^2 + 75x - 28125 = 0

factor this quadratic equation to get:

x = -93.75 or x = 75

x can't be negative, so x = 75 or not at all.

when x = 75, .....

xp = 1875 becomes 75p = 1875.
solve for p to get p = 1875/75 = 25.

when x = 75 and p = 25, .....

(x-15) * (p+4) = 1740 becomes 60 * 29 = 1740 which becomes 1740 = 1740, confirming the solution is correct.

the solution is that he bought 75 shares.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

Ahmad brought a number of shares for Rs 1875.he reserved 15 of theme and sold remaining for Rs1740 making a profit of 4 per share on the cost price.how many share did he buy.

Let number of shares be S
Then cost of each share =
Reserving 15 shares means that he had S � 15 remaining
Therefore, he sold each share for
We then get:
1,875(S � 15) = 1,740S � 4S(S � 15) ------ Multiplying by LCD, S(S � 15)

S(4S + 375) � 75(4S + 375) = 0
(S � 75)(4S + 375) = 0
S, or number of shares he purchased = OR S = (ignore)
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