Question

If 3x=5y=4z, then x:y:z is equal to

Answer 1

3x=4y=5z = k 
x= k/3 ,y= k/4, z= k/5 
x : y: z = k/3:k/4: k/5 = 1/3 : 1/4: 1/5 
x: y : z = 20 : 15 : 12

Answer 2

The ratio of x, y and z is$20:12:15.$

Step-by-step explanation:

We have,

3x = 5y = 4z

To find,  x : y : z = ?

Let $3x=5y=4z=k$

∴ $3x = k$⇒x = $\dfrac{k}{3}$

$5y = k$⇒ y =$\dfrac{k}{5}$ and

$4z = k$ ⇒ z $=\dfrac{k}{4}$

∴$x:y:z= \dfrac{k}{3}:\dfrac{k}{5}:\dfrac{k}{4}$

=$\dfrac{1}{3}:\dfrac{1}{5}:\dfrac{1}{4}$

The LCM of 3, 4 and 5 = 60

Multiplyng 60 in numerator, we get

$=\dfrac{60}{3}:\dfrac{60}{5}:\dfrac{60}{4}$

$=20:12:15$

∴$x:y:z=20:12:15$

Hence, the ratio of x, y and z is$20:12:15$.