Among three numbers, the first is twice the second and thrice

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Among three numbers, the first is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is

Let the second number be p.
∴ First number = 2p

∴ Third number =	2p
	3

∴ 2p + p +	2p	= 49.5 × 3
	3

⇒ 6p + 3p + 2p = 49.5 × 9 = 445.5
⇒ 11p = 445.5

⇒ p =	445.4	= 40.5
	11

∴ Required difference = 2p -	2p	=	4p
	3		3

Required difference =	4 × 40.5	= 54
	3

Aliter : Using Rule 15,

Here, a = 2, b =	3	, X = 49.5
	2

First Number =	3ab	X
	1 + b + ab

First Number =	18 × 49.5	= 18 × 4.5
	11

First Number =	18 × 45	= 81
	10

Third Number =	3	X
	1 + b + ab

Third Number = 6 × 4.5 = 27
Difference = 81 – 27 = 54