If the price of 1 dozen pens is reduced by ₹ 6, then 3 more pens will be got for ₹ 30. Calculate the price of 1 dozen pens before the reduction of price.
Let the price of 1 dozen pen at present is ₹ x
∴ In ₹ at present 12\over \text{x} × 30 pens = 360\over \text{x} pens are got
If the price is reduced by ₹ 6 per dozen, then it becomes ₹ (x – 6)
Then for Rs 30 we get 12\over \text{x - 6} × 30 pens = 360\over x - 6
As per question, 360\over \text{x - 6} – 360\over \text{x} = 3
or, 360(1\over \text{x - 6} – 1\over \text{x}) = 3
or, 120 {\text{x - x + 6}\over \text{(x - 6)x}} = 1
or, 120 {6\over \text{(x - 6)x}} = 1
or, 720\over \text{x² - 6x} = 1
or, x² – 6x – 720 = 0
or, x² – 6x – 720 = 0
or, x² – (30 – 24)x – 720 = 0
or, x² – 30x + 24x – 720 = 0
or, x(x – 30) + 24(x – 30) = 0
or, (x – 30)(x + 24) = 0
either x – 30 = 0 or x + 24 = 0
⇒ x = 30 or x = -24
But the price of pens cannot be negative, so x ≠ -24, hence x = 30
Hence, before the reduction of prices, the price of 1 dozen pens was Rs 30.
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