Question

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional.

• A. 7
• B. 8
• C. 5
• D. 3

Answer 1

The correct option is D

3

Let x to be added to each number then (6 + x), (15 + x), (20 + x) and (43 + x) are in proportion.

$\therefore \frac{6+x}{15+x}=\frac{20+x}{43+x}$

(6 + x) (43 + x) = (20 + x)(15 + x)

258 + 6x + 43x + $x^2$ = 300 + 20x + 15x + $x^2$

258 + 49x + $x^2$ = 300 + 35x + $x^2$

49x + $x^2$ - 35x - $x^2$ = 300 - 258

14x = 42

$x=\frac{42}{14}$

x = 3

Hence, required number is 3.