Correct Answer - Option 4 : 45
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.
