a businessman bought some otems for rs. 7500 . he kept 5 items for himself & sold remaining items at a profit of 25 rs. per item from the amount received in his deal he could buy 6 more items find the original price of each item.
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Let the number of items bought be x.
Total cost of x item is Rs 7500.
(i) Then, price of each items
Number of items sold after keeping 5 for himself = x-5
Profit per item = Rs 25
Then, total profit = (Profit per item) × (Total number of items sold) =25(x-5)
With the profit amount he could buy 6 more items than the number of items he bought previously.
Therefore, from the total profit amount, he could buy (6+5)=11 items, because he sold only (x-5) items.
Then, total cost of 11 items = total profit =25(x-5)
(ii) Then, price of each items
Both (i) and (ii) represents the cost of each item, then the two must be equal.
According to problem,
[tex]\\ 0=x^2-5x-3300 \\ x^2-5x-3300=0 \\ \text{Applying quadratic formula: }\\ x= \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-3300)}}{2(1)} \\ x= \frac{5\pm\sqrt{25+13200}}{2}[/tex]
[tex]x=\frac{5+115}{2} \text{ or }x=\frac{5-115}{2} \\ x=\frac{120}{2} \text{ or }x=\frac{-110}{2} \\ x=60 \text{ or }x=-55 \\[/tex]
The number of items cannot be negative, so we reject x=-55.
Therefore, the number of items bought=x=60.
Total cost of 60 items is Rs7500.
Cost of each item
Answer: Rs 125
Total cost of x item is Rs 7500.
(i) Then, price of each items
Number of items sold after keeping 5 for himself = x-5
Profit per item = Rs 25
Then, total profit = (Profit per item) × (Total number of items sold) =25(x-5)
With the profit amount he could buy 6 more items than the number of items he bought previously.
Therefore, from the total profit amount, he could buy (6+5)=11 items, because he sold only (x-5) items.
Then, total cost of 11 items = total profit =25(x-5)
(ii) Then, price of each items
Both (i) and (ii) represents the cost of each item, then the two must be equal.
According to problem,
[tex]\\ 0=x^2-5x-3300 \\ x^2-5x-3300=0 \\ \text{Applying quadratic formula: }\\ x= \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x=\frac{-(-5)\pm\sqrt{(-5)^2-4(1)(-3300)}}{2(1)} \\ x= \frac{5\pm\sqrt{25+13200}}{2}[/tex]
[tex]x=\frac{5+115}{2} \text{ or }x=\frac{5-115}{2} \\ x=\frac{120}{2} \text{ or }x=\frac{-110}{2} \\ x=60 \text{ or }x=-55 \\[/tex]
The number of items cannot be negative, so we reject x=-55.
Therefore, the number of items bought=x=60.
Total cost of 60 items is Rs7500.
Cost of each item
Answer: Rs 125
rishilaugh:
thanks
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