Question

The average of 11 results is 60. If the average of first six results is 58 and that of the last six is 63. Find the sixth result.

• A. $66$
• B. $70$
• C. $78$
• D. $85$

Answer 1

The correct option is A $66$

Given that average of $11$ results is $60$

Let the results be $r_1,r_2,...r_{11}$

Therefore, $\frac{r_1+r_2+...+r_{11}}{11}=60$

$⟹r_1+r_2+...+r_{11}=11\times 60=660$ -------(1)

Average of first $6$ is $58$

$⟹\frac{r_1+r_2+...+r_6}{6}=58$

$⟹r_1+r_2+...+r_6=58\times 6=348$ -------(2)

Average of last $6$ is $63$

$⟹\frac{r_6+r_7+...+r_{11}}{6}=63$

$⟹r_6+r_7+...+r_{11}=63\times 6=378$

$⟹r_7+...+r_{11}=378-r_6$-------(3)

substituting (2) and (3) in (1) we get

$348+378-r_6=660$

$⟹726-r_6=660$

$⟹r_6=66$

Therefore, the sixth result is $66$.