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प्रश्न
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
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उत्तर
Let the original list price of the toy be Rs. x .
Then, the number of toys brought for Rs.360 `=360/x`
According to question, reduced list price of the toys = Rs. (x - 2).
Therefore, the number of toys brought for Rs.360 `=360/(x-2)`
It is given that
`360/(x-2)-360/x=2`
`360x-360(x-2)/((x-2)x)=2`
`(360x-360x+720)/(x^2-2x)=2`
`720/(x^2-2x)=2`
`720/2=x^2-2x`
360 = x2 - 2x
x2 - 2x - 360 = 0
x2 + 18x - 20x - 360 = 0
x(x + 18) - 20(x + 18) = 0
(x + 18)(x - 20) = 0
x + 18 = 0
x = -18
Or
x - 20 = 0
x = 20
Because x cannot be negative.
Thus, x = 20 is the require solution.
Therefore, the original list price of the toy be x = Rs. 20
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