
Shortcut Trick
To find the number to be added to a, b, c, d for proportion, use the formula: x = (bc − ad) ÷ [(a + d) − (b + c)]
Given a = 12, b = 20, c = 28, d = 44.
x = (20 × 28 − 12 × 44) ÷ [(12 + 44) − (20 + 28)]
x = (560 − 528) ÷ (56 − 48)
x = 32 ÷ 8 = 4
∴ The correct answer is 4.

Alternate Method
Given: Numbers 12, 20, 28, and 44.
Formula Used: If (a + x), (b + x), (c + x), and (d + x) are in proportion, then (a + x) ÷ (b + x) = (c + x) ÷ (d + x).

Let the number to be added be x.
⇒ (12 + x) ÷ (20 + x) = (28 + x) ÷ (44 + x)
Cross-multiplying the terms:
⇒ (12 + x)(44 + x) = (20 + x)(28 + x)
⇒ 528 + 12x + 44x + x2 = 560 + 20x + 28x + x2
⇒ 528 + 56x = 560 + 48x
⇒ 56x − 48x = 560 − 528
⇒ 8x = 32
⇒ x = 32 ÷ 8 = 4
∴ The correct answer is 4.

Additional Information
Continued Proportion
Three numbers a, b, c are in continued proportion if a:b = b:c, which implies b2 = ac.
Fourth Proportional
In the proportion a:b = c:d, the term d is called the fourth proportional, calculated as d = (b × c) ÷ a.
Mean Proportional
The mean proportional between two numbers a and b is given by the square root of their product, √(a × b).
Invertendo Property
If a:b = c:d, then by the invertendo property, b:a = d:c.