Question

The average weight of n persons in a group was 68.4 kg. Later on, 5 persons having weights 59.2 kg, 60.4 kg, 62 kg, 76.4 kg and 78 kg joined the group. As a result, the average weight of all persons in the group decreased by 0.12 kg. The value of n is:
1. 50
2. 40
3. 35
4. 45

Answer 1

Correct Answer - Option 4 : 45

Given:

Average weight of n persons = 68.4 kg 

Weight of 5 new persons = 59.2 kg, 60.4 kg, 62 kg, 76.4 kg, and 78 kg

Formula used:

Total weight = Average weight × Number of persons

Calculation:

Total weight initially = 68.4n

Sum of 5 new persons weight = 59.2 + 60.4 + 62 + 76.4 + 78 = 336 kg

New number of person = (n + 5)

New average of (n + 5) persons = 68.4 - 0.12 = 68.28 kg

According to question,

⇒ 68.4n + 336 = (n + 5) × 68.28

⇒ 68.4n + 336 = 68.28n + 341.4

⇒ 68.4n - 68.28n = 341.4 - 336

⇒ 0.12n = 5.4

⇒ 5.4/0.12 = 540/12 = 45

∴ The value of n is 45.