In a group there are 5 singers, 3 dancers, 2 artists, 1 musician, 1 guitarist…
2026
In a group there are 5 singers, 3 dancers, 2 artists, 1 musician, 1 guitarist and 1 teacher. The average height of the above mentioned people reduces by 2cm if I replace the guitarist with a joker. Find the height of the joker, if the height of the guitarist is 184 cm.
- A.
154 cm
- B.
171 cm
- C.
158 cm
- D.
160 cm
Attempted by 11 students.
Show answer & explanation
Correct answer: C
Concept: When one member of a group is replaced by another, the change in the group's average is governed by: Total change in sum = (change in average) × (number of members), and since only one member differs, this total change equals the difference between the outgoing and incoming member's values.
Count the total number of people in the group: 5 singers + 3 dancers + 2 artists + 1 musician + 1 guitarist + 1 teacher = 13.
The average height falls by 2 cm after the guitarist is replaced by the joker, so the total sum of heights falls by 13 × 2 = 26 cm.
Since every other person's height is unchanged, this 26 cm drop in the sum equals (guitarist's height − joker's height).
So joker's height = guitarist's height − 26 = 184 − 26 = 158 cm.
Cross-check: with the joker at 158 cm, the sum decreases by 184 − 158 = 26 cm across 13 people, which is a drop of 26 ÷ 13 = 2 cm in the average — exactly matching the given information.
Hence, the height of the joker is 158 cm.