Question

The average of 19 numbers is 38. The
average of first 10 of these numbers
is 39 and the last 10 of these numbers
is 36. What is the 10th number?​

Answer 1

Answer:

10 th number = 28

Step-by-step explanation:

Let 10 th number be x.

Sum = Average * No. of values

sum of first 10 + sum of last 10 - x = sum of all 19 numbers

$10 \times 39 + 10 \times 36 - x = 19 \times 38$

$x = 28$

10 th number = 28

Answer 2

Answer:

The 10th number is 28.

Step by step explanation:

We know that average = Sum of all the numbers / Total number of numbers

It is given that that the average of 19 numbers is 38.

38 = Sum of all the numbers / 19

Sum of all the numbers = 38 × 19

= 722

Now, average of the first 10 numbers is 39

Sum of the first 10 numbers = 10 × 39

= 390

It is given that the average of last 10 numbers is 36.

Therefore, the sum of the last 10 numbers = 36 × 10

= 360

Now, there are total 19 numbers but they have given us the average of first and last 10 numbers, if there were 20 numbers in total then we just had to add the average of first 10 numbers and average of last 10 numbers. But there are 19 numbers. So, in order to find the 10th number we will subtract the average of the 19 numbers from the sum of the average of the first and last 10 numbers.

( 390 + 360 ) - 722

750 - 722

28

Ans. The 10th number is 28.