Amount = Principal + Interest

Interest = Amount - Principal

Amount = GH₵ 500.00

Principal = GH₵ 312.50

Interest = GH₵ 500.00 - GH₵ 312.50 = GH₵ 187.5

Let T = number of years.

Rate = 4

$\frac{\mathrm{312.50\; x\; T\; x\; 4}}{100}$ = 187.5

Get rid of the fraction by multiplying both sides by the denominator, 100

100 x $\frac{\mathrm{312.50\; x\; T\; x\; 4}}{100}$ = 187.5 x 100

312.50 x T x 4 = 187.5 x 100

Divide both sides by 312.50 x 4

T = $\frac{\mathrm{187.5\; x\; 100}}{\mathrm{312.50\; x\; 4}}$ = 15 years

∴ Number of years = 15 years

Let y = amount invested at 10%

The amount invested at 11% is 140% of the amount invested at 10%

Amount invested at 11% = $\frac{140}{100}$ x y = 1.4y

3$\frac{1}{2}$ years = 3.5 years

Time (T) = 3.5

Interest at 11%

Principal = 1.4y

Rate = 11%

Interest at 11% = $\frac{\mathrm{1.4y\; x\; 3.5\; x\; 11}}{100}$

Interest at 11% = $\frac{\mathrm{53.9y}}{100}$

Interest at 11% = 0.539y

Interest at 10%

Principal = y

Rate = 10%

Interest at 10% = $\frac{\mathrm{y\; x\; 3.5\; x\; 10}}{100}$

Interest at 10% = $\frac{\mathrm{35y}}{100}$

Interest at 10% = 0.35y

Total interest = Interest at 11% + Interest at 10%

Total interest = GH₵ 22,580.60

22580.60 = 0.539y + 0.35y

22580.60 = 0.889y

Divide both sides by 0.889

y = $\frac{22580.60}{0.889}$

y = 25400

Amount invested at 10% = GH₵ 25,400

Amount invested at 11% = 1.4y = 1.4 x y

Amount invested at 11% = 1.4 x 25400 = GH₵ 35,560

Note: 1 mark is deducted for answers without unit.