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The average of 40 numbers is 48.2. The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5. The 38th number is 1 more than the 39th number, and the 39th number is 3 less than the 40th number. What is the average of the 39th and 40th numbers?

The average of 40 numbers is 48.2. The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5. The 38th number is 1 more than the 39th number, and the 39th number is 3 less than the 40th number. What is the average of the 39th and 40th numbers? Correct Answer 47.5

Given:

The average of 40 numbers is 48.2.

The average of the first 15 numbers is 45 and that of the next 22 numbers is 50.5.

The 38th number is 1 more than the 39th number, and the 39th number is 3 less than the 40th number.

Concept used:

Sum (Total) = Average × Number of elements

Calculation:

The sum of first (15 + 22) = 37 numbers

⇒ (15 × 45) + (22 × 50.5)

⇒ 1786

Let the 39th number be P.

Hence, the 38th & 40th numbers are (P + 1) and (P + 3) respectively.

According to the question,

1786 + (P + 1) + P + (P + 3) = 40 × 48.2

⇒ 3P = 138

⇒ P = 46

⇒ P + 3 = 49

Average of the 39th and 40th numbers = (46 + 49) ÷ 2 = 47.5

∴  47.5 is the average of the 39th and 40th numbers.

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