Question

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.

Answer 1

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.