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प्रश्न
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
उत्तर
Amount spent = Rs. 2800
Price of each plant = Rs. x
Reduced price = Rs. (x – 1)
No. of plants in first case = `(2800)/x`
No. of plants received in second case = `(2800)/x + 10`
Amount paid = Rs. 2730
According to the condition,
`(2800/x + 10)(x - 1)` = 2730
⇒ `((2800 + 10x)(x - 1))/x` = 2730
⇒ (2800 + 10)(x – 1) = 2730x
⇒ 2800x – 2800 + 10x2 – 10x – 2730 = 0
⇒ 10x2 + 2800x – 10x – 2730x – 2800 = 0
⇒ 10x2 + 60x – 2800 = 0
⇒ x2 + 60x – 280 = 0 ...(Dividing by 10)
⇒ x2 + 20x – 14x – 280 = 0
⇒ x(x + 20) – 14(x + 20) = 0
⇒ (x + 20)(x – 14) = 0
Either x + 20 = 0,
then x = –20,
but it is not possible as it is in negative.
or
x – 14 = 0,
then x = 14.
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