If the price of oranges was raised by \(\frac{1}{2}\)k per orange. The number of oranges a customer can buy for N2.40 will be less by 16. What is the present price of an orange?

A.

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

B.

\(\frac{2}{15}\)

C.

5\(\frac{1}{3}\)

D.

20

Correct answer is A

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