Of the three numbers, the first is 3 times the second and

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Of the three numbers, the first is 3 times the second and the third is 5 times the first. If the average of the three numbers is 57, the difference between the largest and the smallest numberis

1. 9
2. 18
3. 126
4. 135

Correct Option: C

Let second number be n.
∴ The first number = 3n
and the third number = 15n
The average of the three numbers = 57
Now, n + 3n + 15n = 3 × 57
⇒ 19n = 3 × 57

⇒ n =	3 × 57	= 9
	19

∴ Required difference = 15n – n = 14n = 14 × 9 = 126
Second method to solve this question with the help of given formulas :
a = 3, b = 5, X = 57

First number =	3ab	X
	1 + b + ab

First number =	3 × 3 × 5	× 57
	1 + 3 + 15

First number =	45	× 57 = 135
	19

Second number =	3b	× X
	1 + b + ab

Second number =	3 × 5	× 57
	1 + 3 + 15

Second number =	15	× 57 = 45
	19

Third number =	3	× X
	1 + b + ab

Third number =	3	× 57 = 9
	19

Required result = 135 – 9 = 126