The average height of 35 telecom towers which are arranged in an ascending order is 284 m. If the average height of first 17 telecom towers is 284 m and that of last 17 telecom towers is 286 m, then what is the height of 18th telecom tower? (In m)

Question

Question

This question was previously asked in

OSSC CGL 2022 Official Paper (Held on: 13th Oct Shift 2)

Answer 1

Given:

Average of 35 towers = 284 m

Average of 1st 17 towers = 284 m

Average of last 17 towers = 286 m

Concept used:

\(Average = {Sum\; of \;observations \over Total \;number\; of\; observations}\)

Calculation:

Average of 1 to 17 = \({1\; to\; 17 \over 17} = 284\) ----- (1)

Average of 1 to 17 = 4828

Average of 18 to 34 = \({18\; to\; 34 \over 17} = 286\) ----- (2)

Average of 18 to 34 = 4862

From the given data, towers are arranged in ascending order

\(284 = {18\; to\; 34 \;+\; 1 \;to \;17 \;+ \;18th\over 35}\) ----- (3)

Substitute (1) and (2) in (3)

284 × 35 = 4862 + 4826 + 18th

9940 = 9690 + 18th

18th = 9940 - 9690

18th = 250

∴ The height of 18th telecom tower is 250m.