Method I

Profit % = $\frac{\mathrm{Profit}}{\mathrm{Cost\; Price}}$ x 100%

Selling Price = Cost Price + Profit
Profit = Selling Price - Cost Price

Profit % = $\frac{\mathrm{Selling\; Price\; -\; Cost\; Price}}{\mathrm{Cost\; Price}}$ x 100%

Let c = Cost Price

Profit % = $\frac{\mathrm{Selling\; Price\; -\; c}}{\mathrm{c}}$ x 100%

Profit % = 20
Selling Price = GH₵ 48.00

20 = $\frac{\mathrm{48\; -\; c}}{\mathrm{c}}$ x 100

20 = $\frac{\mathrm{48\; x\; 100\; -\; c\; x\; 100}}{\mathrm{c}}$

20 = $\frac{\mathrm{4800\; -\; 100c}}{\mathrm{c}}$

Multiply both sides by c

20 x c = 4800 - 100c
20c + 100c = 4800
120c = 4800

Divide both sides by 120 for c to stand alone.

c = $\frac{4800}{120}$ = 40

Note: The zeros in 4800 and 120 cancel each other. 12 divides itself once and 480, 40 times.

Cost Price = GH₵ 40

Method II

Selling Price = Cost Price + Profit
Selling Price % = Cost Price % + Profit %
Cost Price % = 100%
Selling Price % = 100% + Profit %

Profit % = 20%

Selling Price % = 100% + 20%
Selling Price % = 120%

Selling Price = GH₵ 48

If 120% = GH₵ 48
100% = $\frac{\mathrm{GH₵\; 48\; x\; 100\%}}{\mathrm{120\%}}$ = GH₵ 40

Profit Percentage = Profit/Cost Price x 100

Selling Price = Cost Price + Profit

Profit = Selling Price - Cost Price

Let x = Cost Price

Profit = Selling Price - x

Selling Price = 44

Profit = 44 - x

Profit Percentage = Profit/Cost Price x 100

Profit Percent = 10%

Multiply both sides of the equations by x

10 x x = (44 - x) x 100

10 x x = 44 x 100 - x x 100

10x = 4400 - 100x

Solve for x

10x + 100x = 4400

110x = 4400

Divide both sides of the equation by 110

x = 40

Cost price = GH₵ 40.00

ALTERNATIVELY

Cost Price Percentage = 100%

Selling Price Percentage = Profit % + Cost Price Percentage

Profit % = 10%

Selling Price % = 10% + 100% = 110%

Selling Price = 44

Let x = Cost Price

110% (Selling Price Percentage) = 44

100% (Cost Price Percentage) = x

Cross multiply and solve for the value of x

x x 110 = 44 x 100

Divide both sides by 110

x = 4400/110

x = 40

Cost Price = GH₵ 40.00

Profit = Selling Price - Cost Price

Profit percent (%) is the amount of the profit expressed in terms of percentage. The profit is based on the cost price, hence the formula to profit % is (Profit/Cost Price) x 100

But profit = Selling Price - Cost Price

Hence profit % = ([Selling Price-Cost Price]/Cost Price) x 100

From the question, cost price (bought) = 1500

Profit % = 20%

Selling price = ?

Let the selling price be x

Get rid of the denominator by multiplying both sides of the equation by the L.C.M

Every number is divisible by 1, hence 20 = 20/1

The L.C.M of 1500 and 1 is 1500, hence multiply both sides by 1500 and cancel out

100 x (x-1500) = 20 x 1500

100 x x - 100 x 1500 = 30000

100x - 150000 = 30000

100x = 30000 + 150000

100x = 180000

Divide both sides by 100

x = 1800

Profit = Selling Price - Cost Price

Total cost price for the 100 yams = 100 x GH₵ n = GH₵ 100n

Total selling price for the 100 yams = 100 x GH₵ m = GH₵ 100m

Profit = Selling Price - Cost Price

Profit = GH₵ 100m - GH₵ 100n

Factorize GH₵ 100 out

Profit = GH₵ 100(m - n)