Question

the Arithmetic mean of 9 items is 15 if one more item is added to the series the am become 16 the value of 10th item is​

Answer 1

mean of 9 items =15

so sum of the 9 items =9×15=135

Now, mean of 10 items=16

so sum of 10 items=16 ×10=160

So, the 10th itme=160-135= 25

Hope it helps.

Answer 2

Mean of 9 items = 15

Let the sum of 9 items = x

As we know,

$mean = \frac{sum \: of \: observations}{total \: observations}$

Then,

$\frac{x}{9} = 15$

=> x = 9×15 = 135

Now, one more number is added

Let that number = y

Then,

$\frac{135 + y}{10} = 16$

=> 135 + y = 160

=> y = 160 - 135

=> y = 25

The last item (10th item) = 25

$\green{\mathfrak{Last\:item=25}}$