4 4.2 Calculate the value of a if: a $$ 0,4=3: 6 $$ $$ \qquad $$ $$ \qquad $$ 4.3 Increase 5200 kg in the ratio $$ 2: 5 $$ $$ \qquad $$ $$ \qquad $$ 4.4 Share 90 sweets in the following ratio $$ 5: 3: 7 $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3) [9] QUESTION 5 5.1 It takes 7 gardeners 8 hours to plant 1680 seedlings on a plece of land. Calculate (in hours and minutes) how long it would take 12 gardeners to plant the same seedlings. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ 5.2 A car travelling at a constant speed travels 30 km in 15 minutes. How far will it travel in 2 hours 12 minutes if it continues at the same constant speed? $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ (3 5.3 R600 is invested for 3 years at $$ 5 \% $$ p.a. Find the simple interest eamed. $$ \qquad $$ $$ \qquad $$ $$ \qquad $$

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**4.2**  
We are given the proportion  
$$
\frac{a}{0.4}=\frac{3}{6}.
$$  
Solve for $$ a $$:  
$$
a = 0.4\times \frac{3}{6} = 0.4\times 0.5 = 0.2.
$$

**4.3**  
The phrase “increase 5200 kg in the ratio $$2:5$$” means that the original quantity represents 2 parts and the new, increased quantity represents 5 parts. Let one part be $$ x $$. Then:  
$$
2x = 5200 \quad \Longrightarrow \quad x = \frac{5200}{2} = 2600.
$$  
The increased (new) total is:  
$$
5x = 5\times 2600 = 13000\text{ kg}.
$$

**4.4**  
Divide 90 sweets in the ratio $$5:3:7$$. The sum of the parts is:  
$$
5+3+7=15.
$$  
Now calculate each share:  
- First share:  
  $$
  \frac{5}{15}\times 90=30.
  $$  
- Second share:  
  $$
  \frac{3}{15}\times 90=18.
  $$  
- Third share:  
  $$
  \frac{7}{15}\times 90=42.
  $$

**5.1**  
Seven gardeners take 8 hours to plant 1680 seedlings. Total work in gardener-hours is:  
$$
7\times 8=56 \text{ gardener-hours}.
$$  
For 12 gardeners, the time needed is:  
$$
\text{Time}=\frac{56}{12}\approx 4.6667 \text{ hours}.
$$  
To convert the decimal into minutes:  
$$
0.6667 \times 60\approx 40 \text{ minutes}.
$$  
Thus, it takes approximately 4 hours and 40 minutes.

**5.2**  
A car travels 30 km in 15 minutes. Its speed is:  
$$
\frac{30\,\text{km}}{15\,\text{min}}=2\,\text{km/min}.
$$  
Convert 2 hours 12 minutes entirely into minutes:  
$$
2\,\text{hours }12\,\text{min}=2\times 60+12=132\,\text{min}.
$$  
Distance traveled in 132 minutes is:  
$$
2\,\text{km/min}\times 132\,\text{min}=264\,\text{km}.
$$

**5.3**  
The simple interest formula is:  
$$
\text{Interest} = P\times r \times t,
$$  
where $$P=600$$, $$r=5\%$$ per annum (i.e. $$0.05$$), and $$t=3$$ years. Thus,  
$$
\text{Interest}=600\times 0.05 \times 3=600\times0.15=90.
$$
So, the simple interest earned is R90.
**4.2** $$ a = 0.2 $$ **4.3** New total weight = 13,000 kg **4.4** First share: 30 sweets Second share: 18 sweets Third share: 42 sweets **5.1** Time taken = 4 hours 40 minutes **5.2** Distance traveled = 264 km **5.3** Simple interest earned = R90

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