Question : Find the value of $k$, if 5 : $k$ :: 30 : 42.
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 9
Correct Answer: 7
Solution :
5 ∶ $k$ ∶∶ 30 ∶ 42
$\frac{a}{b}= \frac{c}{d}$.......(1)
The equation is 5 ∶ $k$ ∶∶ 30 ∶ 42
On comparing the above equation with (1)
We get, a=5, b=$k$, c=30 and d= 42
Put the value of a, b, c, d in eq (1), we get
⇒ $\frac{5}{k}= \frac{30}{42}$
⇒ $\frac{1}{k}= \frac{1}{7}$
On the reciprocal of the above equation, we get
⇒ k=7
$\therefore$ The value of $k$ is 7.
Hence, the correct answer is 7.
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