Page 133 - Start Up Mathematics_7

Example 14: Convert each part of the ratio to percentage: (a) 4 : 1 (b) 1 : 1 : 3

Solution: (a) 4 : 1
Now, 4 + 1 = 5 is the total of two parts.
4 1
⇒ and are the parts.
5 5
4 4 1 1
5
5 = × 100 % = 80% and = × 100 % = 20%
5
5
(b) 1 : 1 : 3
Now, 1 + 1 + 3 = 5 is the total of all parts.
1 1 3
⇒ , and are the parts.
5 5 5
1 1 1 1
5
5
5 = × 100 % = 20%, = × 100 % = 20%
5
3 3
and = × 100 % = 60%
5 5
Example 15: When a sweet dish is made, the ratio of milk : sugar is 3 : 2. What percentage of
such a mixture would be milk and what percentage would be sugar?
Solution: In terms of ratio, milk : sugar = 3 : 2
2
3
Now, 3 + 2 = 5 is the total of both parts which means part is milk and part is
5
sugar. 5
3
Therefore, percentage of milk would be × 100 % = 60%.
5
2
Percentage of sugar would be × 100 % = 40%.
5

Example 16: (a) Chalk contains calcium, carbon and oxygen in the ratio 10 : 3 : 12. Find the
percentage of calcium in chalk.
(b) If in a stick of chalk, carbon is 5 g, what is the mass of the chalk stick?
Solution: (a) Calcium : carbon : oxygen = 10 : 3 : 12

Total parts = 10 + 3 + 12 = 25
10 3 12
Calcium = , carbon = and oxygen =
25 25 25

10
Percentage of calcium in chalk = × 100 % = 40%
25
3
(b) Percentage of carbon in chalk = × 100 = 12%
25
12% of mass of chalk stick = 5 g

12
100 × Mass of the chalk stick = 5
5 × 100
∴ Mass of the chalk stick = = 41.66 g
12

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