Which number when added to each of the numbers 6, 7, 15,

Which number when added to each of the numbers 6, 7, 15, 17 will make the resulting numbers proportional ?

Let required number be x.

∴	6 + x	=	15 + x
	7 + x		17 + x

⇒ 102 + 17x + 6x + x²
= 105 + 7x + 15x + x²
⇒ 23x – 22x = 105 – 102
⇒ x = 3
Note : It is convenient to solve it orally using options

6 + 3	=	15 + 3	⇒	9	=	18
7 + 3	=	17 + 3	⇒	10	=	20

Second Method :

Required Number =	bc − ad
	(a + d) − (b + c)

Where a = 6, b = 7, c = 15, d = 17

=	7 × 15 − 6 × 17
	(6 + 17) − (7 + 15)

=	105 − 102	= 3
	23 − 22