27. Step 1: Identify the cost price and profit. Cost Price (CP) = sh. $35000$ Profit = sh. $7000$ Step 2: Calculate the percentage profit. The formula for percentage profit is: $$ \text{Percentage Profit} = \frac{\text{Profit}}{\text{Cost Price}} \times 100\% $$ Substitute the given values: $$ \text{Percentage Profit} = \frac{7000}{35000} \times 100\% $$ Step 3: Simplify the fraction. $$ \text{Percentage Profit} = \frac{7}{35} \times 100\% $$ $$ \text{Percentage Profit} = \frac{1}{5} \times 100\% $$ $$ \text{Percentage Profit} = 20\% $$ The percentage profit made by Mutua is $\boxed{20\%}$. 28. a) How much did he pay for the items? Step 1: Calculate the cost of each item. • Cost of sugar: $2 \text{ kg} \times \text{sh. } 140/\text{kg} = \text{sh. } 280$ • Cost of wheat flour: $1 \text{ packet} \times \text{sh. } 170/\text{packet} = \text{sh. } 170$ (assuming 2.2 kg packet is one unit) • Cost of cooking oil: $2 \text{ litres} \times \text{sh. } 320/\text{litre} = \text{sh. } 640$ • Cost of soap: $3 \text{ bars} \times \text{sh. } 120/\text{bar} = \text{sh. } 360$ Step 2: Calculate the total cost of all items. $$ \text{Total Cost} = 280 + 170 + 640 + 360 $$ $$ \text{Total Cost} = 450 + 640 + 360 $$ $$ \text{Total Cost} = 1090 + 360 $$ $$ \text{Total Cost} = \text{sh. } 1450 $$ He paid $\boxed{\text{sh. } 1450}$ for the items. b) If he paid using a two sh. 1000 note. How much balance did he receive? Step 1: Calculate the total amount paid. Amount Paid = $2 \times \text{sh. } 1000 = \text{sh. } 2000$ Step 2: Calculate the balance received. Balance = Amount Paid - Total Cost $$ \text{Balance} = 2000 - 1450 $$ $$ \text{Balance} = \text{sh. } 550 $$ He received a balance of $\boxed{\text{sh. } 550}$. 29. Step 1: Identify the relationship between the angles. The angles $20^\circ$, $80^\circ$, and $m$ are adjacent angles on a straight line. The sum of angles on a straight line is $180^\circ$. Step 2: Set up the equation. $$ 20^\circ + 80^\circ + m = 180^\circ $$ Step 3: Combine the known angles. $$ 100^\circ + m = 180^\circ $$ Step 4: Solve for $m$. $$ m = 180^\circ - 100^\circ $$ $$ m = 80^\circ $$ The value of angle $m$ is $\boxed{80^\circ}$. That's 2 down. 3 left today — send the next one.