A factory buys 10% of its components from suppliers B and the rest from supplier C. It is known that 6% of the components it buys are faulty. of the components brought from suppliers A,9% are faulty and of the components bought from suppliers B, 3% are faulty. find the percentage of components bought from supplier C that are faulty.

A factory buys 10% of its components from supplier A, 30% from supplier B,and the rest from supplier C. it is known that 6% of the components it buys are faulty. of the components bought from supplier A, 9% are faulty and of the components bought from supplier B, 3% are faulty.

find the percentage of the components bought from supplier C that are faulty ?

Step-by-step explanation:

Let x be the total components bought by the factory

Components supplied by A = 10% of x

Components supplied by B = 30% of x

The rest supplied by C:

Percentage supplied by C = 100-(30+10) = 100-40 = 60%

Components supplied by C = 60% of x

% of all faulty components = 6%

Amount of faulty component = 6% of x

faulty components from A= 9%

Amount of faulty component from A= 9% × (6% of x) = 0.0054x

faulty components from B= 3%

Amount of faulty component from A= 3% × (6% of x) = 0.0018x

Amount of faulty component from C = (6% of x) - (0.0054x+0.0018x)

= 0.06x - 0.0072x

= 0.0528x

Let the percentage of the components bought from supplier C that are faulty = y%

y% × 6% of x = 0.0528x

y% × 0.06x = 0.0528x

y% = 0.0528x/0.06x

y% = 0.88 = 88%

The percentage of the components bought from supplier C that are faulty = 88%