Question : Find the value of $k$, if 5 : $k$ :: 30 : 42.
Option 1: 8
Option 2: 7
Option 3: 6
Option 4: 9
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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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