Given:

Average of 3 consecutive numbers = 15

Formula Used:

Average = Sum of terms/Number of terms

Calculations:

Let the 3 consecutive numbers be (x – a), x , (x + a).

Average of 3 consecutive numbers = 15

Average = Sum of terms/Number of terms

⇒ 15 = [(x – a) + x + (x + a)]/3

⇒ 15 × 3 = 3x

⇒ x = 15

3 consecutive numbers = (15 – a), 15, (15 + a)

Multiplying these numbers y 3, we get

Numbers = 3 × (15 – a), 3 × 15, 3 × (15 + a)

⇒ Numbers = (45 – 3a), 45, (45 + 3a)

Sum of these 3 consecutive numbers = (45 – 3a) + 45 + (45 + 3a)

⇒ Sum of these 3 consecutive numbers = 135

Number of terms = 3

Average = 135/3 = 45

∴ The new average when the three numbers are multiplied by 3 is 45.

Short Trick/Topper's Approach:

When all the terms are multiplied by a number, then the average is also multiplied by that number.

Average of 3 consecutive numbers = 15

All 3 numbers are multiplied by 3.

⇒ New average = 3 × 15 = 45 

∴ The new average when the three numbers are multiplied by 3 is 45.