Exercise 8E
Question 1
Ravi’s class has 18 boys and 12 girls. What is its percentage composition?
Sol :
∴Percentage of boys$=\frac{18}{30}\times 100$=60%
∴Percentage of girls$=\frac{12}{30}\times 100$=40%
Question 2
Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in 2 and $\frac{1}{2}$ kg of chalk.
Sol :
Amount of carbon$=\left(2\frac{1}{2}\times \frac{3}{100}\right)$ kg
$=\frac{6}{2}\times \frac{3}{100}=\frac{3}{40}$∴Amount of calcium$=\left(2\frac{1}{2}\times \frac{10}{100}\right)$ kg
$=\left(\frac{5}{2} \times \frac{18}{100}\right)=\frac{1}{4}$
Question 3
An alloy contains 4% tin, 1% zinc and the remaining copper.
(a) What is the percentage composition of the alloy?
Sol :
Percentage of tin=4%
Percentage of zinc=1%
Percentage of copper=(100-5)=95%
(b) Find the mass (in kg) of each metal in 5 tonnes of the alloy.
Sol :
5 tonnes=5000 kg
Mass of tin $=\left(5000 \times \frac{4}{100}\right)$=200 kg
Mass of zinc $=\left(5000 \times \frac{1}{100}\right)$=50 kg
Mass of copper $=\left(5000 \times \frac{95}{100}\right)$=4750 kg
Question 4
A packet of cake mix has the composition of its contents shown on the label. Calculate the percentage composition of the cake mix.
| Nutritional value (per 50 g serve) | |
Protein | 3.5 g |
| Fat | 5.5 g |
Carbohydrates | 27 g |
| Other ingredients | 14 g |
Sol :
∴Percentage of protein$=\frac{3.5}{50} \times 100$=7%
∴Percentage of fat$=\frac{5.5}{50} \times 100$=11%
∴Percentage of carbohydrates$=\frac{27}{50} \times 100$=54%
∴Percentage of other ingredients$=\frac{14}{50} \times 100$=28%
Question 5
The average composition (by weight) of milk is shown in the table.
Ingredients | Percentage |
Carbohydrate | 5 |
Protein | 3 |
Fat | 4 |
| Water | 87 |
| Other | 1 |
(a) How many grams are there of each component in 1 kg of milk?
Sol :
[1 kg=1000 gm]
∴Quantity of carbohydrates$=\left(1000 \times \frac{5}{100}\right)$=50 gm
∴Quantity of protein$=\left(1000\times \frac{3}{100}\right)$=30gm
∴Quantity of fat$=\left(1000 \times \frac{4}{100}\right)$=40 gm
∴Quantity of water$=\left(1000 \times \frac{87}{100}\right)$=870 gm
∴Quantity of other ingredient$=\left(1000 \times \frac{1}{100}\right)$=10 gm
(b) How many grams of proteins are there in 7.5 kg of milk?
Sol :
7.5 kg=7500 gm
∴Quantity of protein$=\left(7500\times \frac{3}{100}\right)$=225 gm
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