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?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 41.5
Average = (Sum of observations)/(Number of observations).
Sum of Ten numbers = 32.5 × 10 = 325.
The sum of the first four numbers = 4 × 25.6 = 102.4.
The sum of the last three numbers = 3 × 38.2 = 114.6
The sum of fifth, sixth and seventh number = 325 - 102.4 - 114.6 = 108.
Let the sixth number be = x
The fifth number = 150% of x = 1.5x
Seventh number = 1.5x + 8.
⇒ x + 1.5x + 1.5x + 8 = 108
⇒ 4x = 100
⇒ x = 25.
Fifth number = 1.5 × 25 = 37.5
Seventh number = 1.5x + 8 = 25 × 1.5 + 8 = 45.5
Required average = (37.5 + 45.5)/2 = 41.5.