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The average weight of some persons in a group is 72 kg. When 5 persons with average weight 66.6 kg join and 13 persons with average weight 75 kg leave the group, the average weight of the persons in the group decreases by 1.65 kg. How many persons were there in the group initially?
1. 40
2. 38
3. 44
4. 48

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Correct Answer - Option 4 : 48

Given:

Average weight of some persons = 72 kg 

Average weight of 5 persons = 66.6 kg 

Average weight of 13 persons = 75 kg 

Formula used:

Average Weight = Total weight/No of persons 

⇒ Total weight = Average weight × No of persons

Calculation:

Let the initial number of persons be = y 

New total weight;

y × 72 + 5 × 66.6 - 13 × 75 = (y + 5 - 13) × (72 - 1.65)

⇒ 72y + 333 - 975 = (y - 8) × 70.35

⇒ 72y - 642 = 70.35y - 562.8 

⇒ 72y - 70.35y = 642 - 562.8 

⇒ 1.65y = 79.2 

⇒ y = 79.2/1.65 

⇒ y = 48 

∴ The inital number of persons = 48

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