Correct Answer: Option A

Explanation

Let x represent the price of an orange and

y represent the number of oranges that can be bought

xy = 240k, y = \(\frac{240}{x}\).....(i)

If the price of an oranges is raised by \(\frac{1}{2}\)k per orange, number that can be bought for N240 is reduced by 16

Hence, y - 16 = \(\frac{240}{x + \frac{1}{2}\)

= \(\frac{480}{2x + 1}\)

= \(\frac{480}{2x + 1}\).....(ii)

subt. for y in eqn (ii) \(\frac{240}{x}\) - 16

= \(\frac{480}{2x + 1}\)

= \(\frac{240 - 16x}{x}\)

= \(\frac{480}{2x + 1}\)

= (240 - 16x)(2x + 1)

= 480x

= 480x + 240 - 32x² - 16

480x = 224 - 32x²

x² = 7

x = \(\sqrt{7}\)

= 2.5

= 2\(\frac{1}{2}\)k

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