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Question

Chalk contains calcium, carbon, oxygen in proportion 10:3:12 .Find the percentage of each in a chalk if the mass of chalk stick is 5gms.


Solution

The proportion of calcium, carbon and oxygen in chalk is given by 10:3:12
ie 10 parts of calcium, 3 parts of carbon and 12 parts of oxygen exist out of a total no of parts given by 10 + 3 + 12 = 25 parts.

ie Fraction of calcium in chalk = 10 / 25
Fraction of carbon in chalk = 3 / 25
Fraction of oxygen in chalk = 12 / 25

Hence, percentage of  calcium in chalk = (10 / 25) * 100
                                                               = 40 %
Percentage of  carbon in chalk = (3 / 25) * 100
                                                               = 12 %
Percentage of  oxygen in chalk = (12 / 25) * 100
                                                               = 48 %

NOTE: The mass of the chalk is not required in calculating the percentage of each component.
However, we can use this information to find the mass of each component in the chalk stick that has a mass of 5 gms.

ie Mass of calcium in 5g chalk = 40 % * 5 = (40/100) * 5
                                                                     =2 g
Mass of carbon in 5g chalk = 12 % * 5 = (12/100) * 5
                                                                     =0.6 g
Mass of oxygen in 5g chalk = 48 % * 5 = (48/100) * 5
                                                                     =2.4 g


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Mathematics

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