If the price of oranges was raised by (frac{1}{2})k per orange. The number of oranges…

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?

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