The average of ten numbers is 32.5. The average of first four numbers is 25.6 and that of the last three numbers is 38.2. The 5th number is 50% more than the 6th number and 8 less than the 7th number. What is the average of 5th and 7th numbers?

The average of ten numbers is 32.5. The average of first four numbers is 25.6 and that of the last three numbers is 38.2. The 5th number is 50% more than the 6th number and 8 less than the 7th number. What is the average of 5th and 7th numbers? Correct Answer 41.5

Given:

The average of ten numbers = 32.5

The average of first four numbers = 25.6

The average of last three numbers = 38.2

The 5^th number is 50% more than the 6^th number and 8 less than the 7^th number

Formula used:

Average = sum of observations/Number of observations

Calculation:

The average of ten number = (10 × 32.5) = 325

The average of first four number = (4 × 25.6) = 102.4

The average of last three number = (3 × 38.2) = 114.6

According to the question

Let the number be x

5^th number is 50% more efficient than the 6^th number = (x × 50/100) = 1x/2

The 6^th number = 2x

The 5^th number = (2x + x) = 3x

The 7^th number = 3x + 8

Now,

⇒ (102.4 + 114.6 + 2x + 3x + 3x + 8) = 325

⇒ (225 + 8x) = 325

⇒ 8x = (325 – 225)

⇒ 8x = 100

⇒ x = (100/8)

⇒ x = 12.5

The average of 5^th and 7^th number = (3x + 3x + 8)/2

⇒ (6x + 8)/2

⇒ 3x + 4

⇒ (3 × 12.5 + 4)

⇒ (37.5 + 4)

⇒ 41.5

∴ The required average is 41.5