Correct Answer - Option 3 : 1.65 meters
Given:
The average height of 9 pipes is 1.8 meters.
The average height of the first 5 pipes is 2.3 meters.
The average height of the last 5 pipes is 1.6 meters.
Formula Used:
Average = sum of total terms/ total number of terms
Calculation:
The average height of 9 pipes is 1.8 meters.
Average = sum of total terms/ total number of terms
⇒ 1.8 = Sum of height of total 9 pipes / 9
⇒ Sum of the height of total 9 pipes = 1.8 × 9
⇒ Sum of the height of total 9 pipes = 16.2 meters.
The average height of the first 5 pipes is 2.3 meters.
⇒ 2.3 = Sum of the height of first 5 pipes / 5
⇒ Sum of the height of the first 5 pipes = 2.3 × 5
⇒ Sum of the height of the first 5 pipes = 11.5 meters. ----(1)
The average height of the last 5 pipes is 1.6 meters.
⇒ 1.6 = Sum of the height of the last 5 pipes / 5
⇒ Sum of the height of the last 5 pipes = 1.6 × 5
⇒ Sum of the height of the last 5 pipes = 8.0 meters. ----(2)
Adding equation (1) and (2)
Sum of the height of the first 5 and the last 5 pipes = 11.5 + 8.0
⇒ Sum of the height of the first 5 and the last 5 pipes = 19.5 meters
But the sum of the height of the total 9 pipes = 16.2 meters.
⇒ The height of the 5th pipe is counted twice
⇒ The height of the 5th pipe = (19.5 – 16.2)/ 2
⇒ The height of the 5th pipe = 3.3 / 2
⇒ The height of the 5th pipe = 1.65 meters
∴ The height of the 5th pipe is 1.65 meters.
