Correct Answer - Option 3 : 67

**Given:**

Average of 10 numbers is 72.8

Average of first 6 numbers is 88.5

Average of last five numbers is 64.4

**Formula Used:**

Average = Sum of all observations/Total number of observations

**Calculations:**

Average of 10 numbers is 72.8

⇒ 72.8 = Sum of all 10 numbers/10

⇒ Sum of all 10 numbers = 72.8 × 10

⇒ Sum of all 10 numbers = 728

Average of first 6 numbers is 88.5

⇒ 88.5 = Sum of first 6 numbers/6

⇒ Sum of first 6 numbers = 88.5 × 6

⇒ Sum of first 6 numbers = 531

Average of last five numbers is 64.4

⇒ 64.4 = Sum of last 5 numbers/5

⇒ Sum of last 5 numbers = 322

Sum of total 11 numbers = Sum of first 6 numbers + Sum of last 5 numbers

⇒ Sum of total 11 numbers = 531 + 322

⇒ Sum of total 11 numbers = 853

But Sum of 10 numbers is 728

Number 6 is counted twice,

⇒ Number 6 = 853 – 728

⇒ Number 6 = 125

Now number 6 is excluded ,

⇒ New sum = 728 – 125

⇒ New sum = 603

Average of remaining 9 numbers,

⇒ Average = Sum of 9 numbers/ 9

⇒ Average = 603/9

⇒ Average = 67

**∴ The average remaining 9 numbers is 67.**