Question

what percentage of a mixture of sand, gravel and cement containing 30% cement should be replaced by pure cement in order to produce a mixture that is 40% cement?

Answer 1

Suppose amount of the mixture is 'A'.

It is given in the question that the mixture contains 30% cement.

Therefore, the amount of cement = (30 / 100)* A = 0.3A

Now, assume 'x' amount of mixture is replaced by pure cement in order to produce a mixture that contains 40% cement.

This means that first, we have removed 'x' amount of mixture and then added 'x' amount of pure cement.

If we remove 'x' amount of mixture the from amount 'A' we will have (A - x) amount of mixture.

the mixture contains 30% cement.

Therefore, the amount of cement in (A - x) amount of mixture = (30 / 100)* (A - x) = (0.3A - 0.3x)

Now, 'x' amount of pure cement is added in (A - x) amount of mixture.

Therefore, the amount of new mixture will become 'A'.

Amount of cement in the new mixture = [(0.3A - 0.3x) + x] = (0.3A - 0.3x + x) = (0.3A + 0.7x)

It is given in the question that the new mixture contains 40% cement.

40% of the new mixture = (40 / 100) * A = 0.4A

Therefore,

0.4A = 0.3A + 0.7x

0.4A - 0.3A = 0.7x

0.1A = 0.7x

A = 7x

x = (A / 7)

Therefore, in order to produce a mixture that contains 40% cement we have to replace (A / 7) amount of the mixture by pure cement.

In percentage

[(A / 7) / A] * 100

= [(1 / 7) * 100]

=(100 / 7)

= 14.286%

Therefore, in order to produce a mixture that contains 40% cement we have to replace 14.286% of the mixture by pure cement.

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