The mean weight of 17 boxes is 92 kg. If 18 new boxes are added, the mean weight increases by 3 kg. What will be the mean weight of the 18 new boxes?

1. 91.8 kg

2. 92.8 kg

3. 97.8 kg

4. 98.8 kg

Total weight of 17 boxes = Mean × Number of boxes

= 92 × 17 = 1564 kg.

If 18 new boxes are added, mean increases by 3 kg.

So, new mean = 92 + 3 = 95 kg.

Total weight of 35 boxes = New mean × Number of boxes

= 95 × 35

= 3325 kg

The weight added by the 18 new boxes = Total weight of 35 boxes - Total weight of 17 boxes

= 3325 - 1564

= 1761 kg.

By formula,

$\text{Mean of 18 boxes} = \dfrac{\text{Weight of 18 boxes}}{\text{ Number of boxes}} \\[1em] = \dfrac{1761}{18} \\[1em] = 97.8 \text{ kg.}$

Hence, option 3 is the correct option.