Question

A businessman bought some items for rs 7500.he kept 5 items for himself and sold the remaining items at profit of RS 30 per item . from amount received in this deal he could buy 4 more items find the original price of each item​

Answer 1

hey mate!

No. of items bought = x

Price per item = y

Total amount paid = x * y = xy = 7500

y = 7500 / x

Total items sold = (x - 5)

Price of each item = (y + 30)

Total revenue received = (x - 5) * (y + 30)

Since he can buy 4 more items from his revenue

(x - 5)(y + 30) - 7500 = 4 * y

(x - 5)[(7500/x) + 30] - 7500 = 4y

(x - 5)[(7500 + 30x) / x ] - 7500 = 4y

(x - 5)(7500 + 30x) - 7500x  = 4xy

7500x + 30x² - 37500 - 150x - 7500x = 4xy

30x² + 7500x - 150x - 7500x  - 37500 = 4(7500)

30x² - 150x - 37500 - 30000 = 0

30x² - 150x - 67500 = 0

30 (x² - 5x- 2250) = 0

x² - 5x - 2250 = 0

x = -45 , +50 (Solving quadratic equation)

Since cost cannot be negative, so x = 50 which is the number of items bought.

The price per item = 7500/50 = 150

Answer 2

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$\sf{\underline{Given:}}$


$\sf{Price\:per\:item}$$=\:y$


$\sf{No.\:of\:items\:bought}$ $=\:x$


$\sf{Total\:amount\:paid,}$ $xy = 7500$


$y = \frac{7500}{x}$


$\sf{Total\:items\:sold}$$= (x - 5)$


$\sf{Price\:of\:each\:item}$ $= (y + 30)$


$\sf{Total\:revenue\:received}$ $= (x - 5) \times (y + 30)$


$\sf{\underline{Since\:he\:can\:buy,}}$


$\sf{4\:more\:items\:from\:his\:revenue.}$


$(x - 5)(y + 30) - 7500 = 4 \times y$


$(x - 5)( \frac{7500}{x} + 30) - 7500 = 4y$


$(x - 5)( \frac{7500 + 30x}{x} ) - 7500 = 4y$


$(x - 5)(7500 + 30x) - 7500x = 4xy$


$7500x + 30 x^{2} - 37500 - 150x - 7500x = 4xy$


${30x}^{2} + 7500x - 150x - 7500x - 37500 = 4(7500)$


${30x}^{2} - 150x - 37500 - 30000 = 0$


$30x^{2} - 150x - 67500 = 0$


$30( {x}^{2} - 5x - 2250) = 0$


${x}^{2} - 5x - 2250 = 0$


$\sf{\underline{Solving\:the\:quadratic\:equation}}$


$\sf{\underline{We\:get,}}$


$x = - 45 \: \: \: \: \: x = 50$


$\sf{\underline{Since\:the\:cost\:cannot\:be\:negative,}}$

$x = - 45$ is discarded.


$\sf{\underline{So,}}$

$x = 50$


$\sf{\underline{Therefore,}}$

$\sf{50\:items\:were\:bought.}$


$\sf{The\:price\:per\:item}$ $\frac{7500}{50} = 150$


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