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Ratio and Proportion

Given that : ...

Question

Given that : $x + y - z + 100 = 350$ . If $x = 2 y$ and $y = 2 z$ , then $z = ?$

A

30

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B

50

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C

70

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D

90

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Solution

The correct option is B $50$
$x + y - z + 100 = 350$ .......(1)
$y = 2 z$ ......(2) (Given)
$∴ x = 2 y = 4 z$ ....(3)
From (1), (2) and (3), we get
$4 z + 2 z - z = 250$
$∴ 3 (2 z) - z = 250$
$∴ 5 z = 250$
$∴ z = 50$
Hence, option B is the correct answer.

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Similar questions

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} x - y - z & 2 x & 2 x 2 y & y - z - x & 2 y 2 z & 2 z & z - x - y \end{matrix} ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x + y + 2 z & x & y z & y + z + 2 x & y z & x & z + x + 2 y \end{matrix} ∣ ∣ ∣ ∣

\frac{x}{2 y + z - x} = \frac{y}{2 z + x - y} = \frac{z}{2 x + y - z}

x + y + z \neq 0

, then what is each ratio equal to.

∣ ∣ ∣ ∣ \begin{matrix} x + y + 2 z & x & y z & y + z + 2 x & y z & x & z + x + 2 y \end{matrix} ∣ ∣ ∣ ∣ = 2 (x + y + z)^{3}

2 x + y + z

- x + 2 y + 2 z

x - y - z

x, y, z > 0

x + y + z = 1,

then the least value of

\frac{2 x}{1 - x} + \frac{2 y}{1 - y} + \frac{2 z}{1 - z}

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