Question

The average of 8 numbers is 99. The difference between the largest two numbers is 18 The average of the remaining 6 numbers is 87 The largest among the 8 is :
1. 126
2. 152
3. 86
4. 144

Answer 1

Correct Answer - Option 4 : 144

Given:

The average of 8 numbers = 99

The difference between the largest two numbers = 18

The average of the remaining 6 numbers= 87

Formula used:

Sum of all observations = Average × Number of observations 

Calculation:

The sum of 8 numbers = 99 × 8 = 792

The sum of remaining 6 numbers = 87 × 6 = 522

⇒ Sum of two numbers = sum of 8 numbers - sum of 6 numbers = 792 - 522 = 270

Let the first largest number = X

and, let the second largest number = Y

⇒ X + Y = 270      ----(1)

According to question, X - Y = 18      ----(2)

On Solving (1) and (2), we get 

⇒ X = 144, Y = 126

∴ The Largest number among 8 numbers is 144.