Index Number:
b) A trader bought ar bags of rice at a cost, c= 24x+103 and sold them at a price.
x = 33x-x^2/20

(1)
Find the expression for the profit.
(i) If 20 bags of rice were sold, calculate the percentage profit.

Question

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MrRoyal MrRoyal · Answer 1 · 2022-06-13T20:28:30+02:00

The expression for the profit is -x^2/30 + 9x - 103 and the percentage profit on 20 bags of rice is 11.1%

The cost and the selling price are given as:

C(x) = 24x + 103

S(x) = 33x - x^2/30

The profit is calculated using:

P(x) = S(x) - C(x)

This gives

P(x) = 33x - x^2/30 - 24x - 103

Evaluate the like terms

P(x) = -x^2/30 + 9x - 103

Hence, the expression for the profit is -x^2/30 + 9x - 103

When x = 20, we have:

Cost: C(20) = 24 * 20 + 103 = 583

Profit: P(20) = -(20)^2/30 + 9(20) - 103 = 64.67

The percentage profit is then calculated as:

Percentage = P(x)/C(x) * 100%

This gives

Percentage = 64.67/583 * 100%

Evaluate

Percentage = 11.1%

Hence, the percentage profit on 20 bags of rice is 11.1%