Answer :

To find the 10th number, we calculate the sums of the first 10 and the last 10 numbers, and then solve for the 10th number by subtracting the total sum of 19 numbers. The 10th number is 25.

To find the 10th number, let's start by calculating the total sum of the 19 numbers and the sum of the first 10 and last 10 numbers:

  • Mean of 19 numbers = 15, so the sum = 19 * 15 = 285
  • Mean of the first 10 numbers = 17, so the sum = 10 * 17 = 170
  • Mean of the last 10 numbers = 14, so the sum = 10 * 14 = 140

Since the 10th number is included in both the first set of 10 numbers and the last set of 10 numbers, its value is effectively counted twice. To find the 10th number (let's call it x), we use the following equation:

(Sum of first 10 numbers + Sum of last 10 numbers) - Total sum of 19 numbers = x

So, (170 + 140) - 285 = x

310 - 285 = x

Therefore, the 10th number is 25.

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