Calculate \( x \) in the following ratio: \[ 2: 4=5,4: 3 \] Write the ratio in its simplest form: \[ 2 \mathrm{~m}: 8 \mathrm{~cm}: 40 \mathrm{~mm} \] AB and Peter bought a house for R575000 as an investment. AB payed R 245000 and Peter payed the rest. They sold the house 5 years later and made a profit of R234 500 . What is the percentage profit that they made? Wher f they share the profit in the same ratio as their respective investments, how nuch profit will Peter receive?

To calculate \( x \) in the given ratio \( 2:4 = 5.4:3 \), we can cross-multiply. This gives us \( 2 \cdot 3 = 4 \cdot 5.4 \), which simplifies to \( 6 = 21.6 \). Finding \( x \) involves solving the proportion, which indicates that while ratios can be interesting, using them can sometimes lead to confusion if not clearly defined! In terms of the simplified ratio of \( 2 \mathrm{~m}: 8 \mathrm{~cm}: 40 \mathrm{~mm} \), we first convert all units to meters: \( 8 \mathrm{~cm} = 0.08 \mathrm{~m} \) and \( 40 \mathrm{~mm} = 0.04 \mathrm{~m} \). The ratio becomes \( 2:0.08:0.04 \), which can then be multiplied by 100 to simplify it to \( 200:8:4 \). Further simplification gives us \( 50:2:1 \). For the profit calculation, AB and Peter initially invested R245,000 and R330,000 respectively (R575,000 - R245,000). They made a profit of R234,500, giving a total amount of R809,500 when sold (R575,000 + R234,500). The percentage profit can be found using the formula \(\frac{\text{profit}}{\text{cost price}} \times 100\): \(\frac{234,500}{575,000} \times 100\) results in a percentage profit of approximately 40.7%. When it comes to sharing the profit proportionally, since AB’s investment is R245,000 and Peter’s is R330,000, their combined investment is R575,000. The share of profits would then be in the ratio of their investments, therefore, Peter’s share would be \(\frac{330,000}{575,000} \times 234,500 = R 138,450\). Voilà, profits shared proportionally!