Question

(x - y + z) : (y - z + 2w) : (2x + z - 10) = 2:3:5 Then ( 3x + 3z - 2w) : w = ?​

Answer 1

I think the correct question would be like,

if ( x - y + z) : (y - z + 2w) : (2x + z - w) = 2 : 3 : 5.

Then find ( 3 x + 3 z - 2 w ) : w.

Solution for this question:-

Let's assume the ratio be 2a : 3a : 5a.

That means,

(x - y + z) = 2a ----(1)

(y - z + 2w) = 3a ----(2)

(2x + z - w) = 5a ---(3)

Since 2a + 3a is equal to 5a, this implies that equation (1) + equation (2) must be equal to equation (3).

( x - y + z ) + ( y - z + 2 w ) = ( 2 x + z - w )

x - y + z + y - z + 2 w = 2 x + z - w

x + 2w = 2 x + z - w

2 w + w = 2 x + z - x

3 w = x + z

Multiply this equation by 3.

9 w = 3 x + 3 z ---(4)

We have to find,

( 3 x + 3 z - 2 w ) : w

Put value of 3 x + 3 z from equation (4)

(9 w - 2 w) : w

7 w : w

7 : 1

So, 7 : 1 would be the correct answer.

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