Question

The mean of $10$ numbers is $12.5$; the mean of the first six is $15$ and the last five is $10$. The sixth number is

• A. $15$
• B. $12$
• C. $18$
• D. None of these

Answer 1

The correct option is A $15$

The sum of firs 6 numbers is

$=15\times 6$
$=90$

Therefore

$x_1+x_2+...x_6=90$ ...(i)

And

The sum of last five number is

$=10\times 5$
$=50$

Therefore

$x_{10}+x_9+x_8...x_6=50$ ...(ii)

Sum of all number is

$=12.5\times 10$
$=125$ ...(iii)

Hence

$i+ii$

$=140$
$=(x_1+x_2+....x_{10)}+x_6$

$=125+x_6$

Or

$x_6=15$.