In a hotel, there are 120 staff members. Their average weight is 62.5 kg. When one of the staff members leaves the hotel, the average weight is reduced by 250 g. Find the weight of the staff member who left the hotel.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 1)

Answer 1

Given:

Total number of staff members = 120

Average weight = 62.5 kg

Reduced average weight = 250g = 0.25 kg

New average weight = 62.25 kg

Formula used:

Average = \(Sum\: of \:weight \:of \:all \:the \:staff \: members \over Total\: no.\: of \:staff \: members \)

Let the weight of that one staff member who left be x,

and addition of weight of other staff be y.

Calculation:

The total weight of all the staff members in the hotel before one of them left is:

120 staff members × 62.5 kg/person = 7500 kg

When one staff member leaves, the total weight of the remaining 119 staff members is:

119 staff members × (62.5 kg - 0.25 kg)

⇒ 119 staff members × 62.25 kg/person 7407.75 kg

⇒ 7407.75 kg

The difference in weight before and after the staff member left is:

7500 - 7407.75 = 92.25 kg

According to the problem statement, this difference in weight is equal to the weight of the staff member who left the hotel, which is x kg.

So, we can write:

92.25 kg = x kg

∴ The weight of the staff member who left the hotel is 92.25 kg.

Shortcut Trick

There are 120 staff members and their average weight 62.5 kg. Now, one member left and average weight decreases by 250 g

It means that member have the extra weight than average is (250 × 119) g = 29750 g = 29.75 kg

So, the staff member's weight is 62.5 + 29.75 = 92.25 kg