Find the value of x in the proportion 69 : 23 :: 63 : x.

Correct option is A

Given:
Proportion: 69 : 23 :: 63 : x
Concept Used:
In a proportion a : b :: c : d, the product of extremes equals the product of means.
​$$a \times d = b \times c$$​​
Solution:
Apply the property to the given values:
​$$69 \times x = 23 \times 63$$​​
Solve for x:
​$$x = \frac{23 \times 63}{69}$$​​
​$$x = \frac{1 \times 63}{3} (\text{Since} \ \ \frac{23}{69} = \frac{1}{3}) \\ \ \\x = 21$$​​
Exam-Hall Method:
Notice the relationship between the first two terms:
​$$\frac{69}{3} = 23$$​​
Apply the same logic to the second pair:
​$$\frac{63}{3} = 21$$​​
So the correct answer is (a)