Question

If x:y= 1: 3, y:z= 5: k, z:t= 2: 5 and t:x= 3: 4 then what is the value of k?

Answer 1

Answer:

k = 1/2

Step-by-step explanation:

As we know,

If a:b = N1 : D1,

b:c = N2:D2,

c:d = N3:D3

then  we can write =>  

a : b : c : d = N1*N2*N3 : D1*N2*N3 : D1*D2*N3 : D1*D2*D3   ----eq(1)

from eq(1)

x : t = 1*5*2 : 3*k*5

x:t = 10 : 15*k

x:t = 2 : 3k

4:3 = 2/k : 3

from here,

2/k = 4

1/k = 2

k = 1/2

just practise this trick and you can find any solutin of this type of question.

Answer 2

Given: $x:y= 1: 3, y:z= 5: k, z:t= 2: 5 \ and \ t:x= 3: 4$

To find: The value of $k$

Solution: According to the given question,

$\frac{x}{y} = \frac{1}{3}$

Using cross multiplication:

∵ $3x = y$   ...(1)

also, $\frac{y}{z} = \frac{5}{k}$                              [Given]

i.e., $ky = 5z$   ...(2)                   [Using cross multiplication]

$\frac{z}{t} = \frac{2}{5}$                                       [Given]

i.e., $5z = 2t$   ...(3)                    [Using cross multiplication]

$\frac{t}{x} = \frac{3}{4}$                                       [Given]

i.e., $4t = 3x$   ...(4)                    [Using cross multiplication]

Now, using (1) and (4)

∵ $y = 3x \ and \ 3x = 4t$

i.e., $y = 3x = 4t$

∴ $y = 4t$  ...(5)

It  can be written as:

∵ $y = 2*2t$

From (3), $2t = 5z$

∴ $y = 2 * 5z = 10z$

Now, putting $y = 10z$ in equation (2)

⇒ $k * 10z = 5z$

⇒ $10 k = 5$

⇒ $k = \frac{5}{10} = \frac{1}{2}$

Hence, the value of  $k$ is $\frac{1}{2}$.