If the average of 6 positive integers is 45 and the difference between the largest and the smallest of these 6 numbers is 18, then what is the minimum value possible for the smallest of these 6 integers?

Correct option is A

Given:

The average of 6 positive integers = 45

The difference between the largest and smallest integers = 18

Formula Used:

Sum of integers =$$\text{Average} \times \text{Number of integers}$$​

Solution:
Let the six numbers be N₁, N₂, N₃, N₄, N₅, N₆

Sum of all the six numbers = 45 × 6 = 270

Let the smallest integer be N₁, and the largest integer be N₆

According to given condition:
N₆ = N₁ + 18 
N₁ + N₂ + N₃ + N₄ + N₅ + N₆ = 270 
N₁ + N₂ + N₃ + N₄ + N₅ + N₁ + 18 = 270 
To the minimum value of N₁, we should keep all the numbers equal to Largest Number =  N₁ + 18.
N₁ + N₁ + 18 + N₁ + 18 + N₁ + 18 + N₁ + 18 + N₁ + 18 = 270  
6N₁ + 90 = 270
6N₁ = 180 
N₁ = 30 
Minimum Value of N₁ = 30