Question: 1. In an examination, a girl gets 35 marks out of 40. Express this result as a percentage.
2. A school football team plays 25 games in a season. They win 17, draw 2 and lose the rest. Express the numbers won, drawn and lost as percentages of the total number, of games played.
3. An airline has a fleet of 80 planes. Of these, 10 are being serviced at any one time. What percentage of the fleet is available for flights?
4. A car manufacturer produces 175000 sports cars a year. They are only available in white, black and red. 52500 are white, 78750 are black and the rest are red. a) What percentage of the cars are black? b) What percentage are white? c) What percentage are red?
1. **Problem:** A girl scores 35 marks out of 40. Find the percentage.
**Formula:** Percentage = $$\frac{\text{Obtained marks}}{\text{Total marks}} \times 100$$
**Calculation:**
$$\frac{35}{40} \times 100 = \frac{35 \times 100}{40}$$
Simplify by canceling common factors:
$$\frac{\cancel{35} \times 100}{\cancel{40}} = \frac{35 \times 100}{40}$$
Actually, 35 and 40 share a factor 5:
$$\frac{\cancel{35}^{7} \times 100}{\cancel{40}^{8}} = \frac{7 \times 100}{8} = 87.5$$
**Answer:** The girl scored 87.5%.
2. **Problem:** A football team plays 25 games: wins 17, draws 2, loses the rest. Find percentages.
Total games = 25
Lost games = 25 - (17 + 2) = 6
Percentage won:
$$\frac{17}{25} \times 100 = 68\%$$
Percentage drawn:
$$\frac{2}{25} \times 100 = 8\%$$
Percentage lost:
$$\frac{6}{25} \times 100 = 24\%$$
**Answer:** Won 68%, Drawn 8%, Lost 24%.
3. **Problem:** Airline has 80 planes, 10 serviced, find percentage available.
Available planes = 80 - 10 = 70
Percentage available:
$$\frac{70}{80} \times 100 = \frac{7}{8} \times 100 = 87.5\%$$
**Answer:** 87.5% of the fleet is available.
4. **Problem:** Manufacturer produces 175000 cars: 52500 white, 78750 black, rest red.
Total cars = 175000
Red cars = 175000 - (52500 + 78750) = 175000 - 131250 = 43750
a) Percentage black:
$$\frac{78750}{175000} \times 100 = \frac{78750 \times 100}{175000}$$
Simplify:
$$\frac{\cancel{78750}^{45} \times 100}{\cancel{175000}^{100}} = \frac{45 \times 100}{100} = 45\%$$
b) Percentage white:
$$\frac{52500}{175000} \times 100 = \frac{52500 \times 100}{175000}$$
Simplify:
$$\frac{\cancel{52500}^{30} \times 100}{\cancel{175000}^{100}} = \frac{30 \times 100}{100} = 30\%$$
c) Percentage red:
$$\frac{43750}{175000} \times 100 = \frac{43750 \times 100}{175000}$$
Simplify:
$$\frac{\cancel{43750}^{25} \times 100}{\cancel{175000}^{100}} = \frac{25 \times 100}{100} = 25\%$$
**Answer:** Black 45%, White 30%, Red 25%.