Find ratio of x:y:z (1) 7x = 8z + 4y (2) 6z = 11y + 5x

Question

Find ratio of x:y:z

(1) 7x = 8z + 4y 
(2) 6z = 11y + 5x

chetan2u · Answer

Pl follow the rules and post question with OA and source mentioned.

At the first look you can see that each statement contains three variables, so each is clearly insufficient as it cannot give relationship between the three variables...

Combined..
From the two equation, you can find relationship between two variables..
Substitute that in any of the equation, you will find relationship between all three..
So sufficient..

C..

This was sufficient without checking for answer as we had two distinct equation..

But if these were in a PS, we would solve in following manner..

(1) 7x = 8z + 4y ......
Multiply by 3....
21x=24z+12y........24z=21x-12y
(2) 6z = 11y + 5x
Multiply by 4..
24z=44y+20x

From the above statements..
21x-12y=44y+20x...
X=56y

Put in equation (1)
7*56y=8z+4y
From this you will get relationship between y and z..

neha1sara · Answer

Can you explain this further?

Bunuel · Answer

Find ratio of x:y:z

(1) 7x = 8z + 4y
(2) 6z = 11y + 5x

Each statement is insufficient on its own. When taken together try to get rid of one of the unknowns to get an equation with two unknowns only. Let's eliminate z. For that, multiply the first equation by 3 and the second equation by 4:
 21x = 24z + 12y
24z = 44y + 20x

Add them:
 21x +24z = 24z + 12y + 44y + 20x;
x = 56y

Substitute in the first equation:
 21*56y = 24z + 12y
2z = 97y

Since y = x/56, then 2z = 97y = 97*x/56, which gives z = 97x/112.

Therefore, x:y:z = x:(x/56):(97x/112) = 1:(1/56):(97/112).

Answer: C.

Find ratio of x:y:z (1) 7x = 8z + 4y (2) 6z = 11y + 5x

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