Question

An amount is divided among X, Y, Z. Amount of Y is average of other two and when amount of Y is reduced by 20% of that of X it becomes equal to that of Z.Find the amount of Z is what percentage of total amount.​

Answer 1

Let the total amount be 100.

Let the amount of X be 'x' and that of Z be 'z'.

So amount of Y is (100 - x - z) since I assumed total amount as 100.

So we are given that : Amount of Y is average of other two.

$100-(x+z) = \frac{x+z}{2}$

$100 = \frac{3(x+z)}{2}$

$x + z = \frac{200}{3}.....(i)$

When amount of Y is reduced by 20% that of X it becomes equal to Z.

$100 -(x+z) - \frac{20x}{100} = z$

$1000 - 10(x+z) - 2x = 10z$

$12x +20z = 1000.....(ii)$

$\small\black\boxed{(i)*12}=> 12x + 12z = 800.....(iii)$

$\small\black\boxed{(ii) - (iii)}=> 8z = 200$

$z = \frac{200}{8} = 25$

That means the amount of Z is 25% of the total amount

Answer 2

Answer:

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