The average weight of eight people is X kg. Two new people joined them with total weight of 151 kg and average weight of all people increased by 3/2 kg. If the weight of lightest people out of two people joined is X-5 kg, the find the difference between weight these two people who joined later.

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Information Given in the Question:
Average weight of 8 people = X kg
Total weight of 8 people = 8X kg

Two new people joined.
Total weight of these two people = 151 kg

Average increases by 3/2 kg

New number of people = 10

Weight of lighter person among the two = X - 5 kg

We need to find the difference between the weights of the two people who joined.

Average = Total Weight / Number of People

New Average = Old Average + Increase

Total Weight = Average × Number of People

Total weight of first 8 people
= 8X

Average increases by 3/2 kg

New average
= X + 3/2

Total weight of all 10 people

= 10 × (X + 3/2)

= 10X + 15

But total weight also equals:

Weight of first 8 people + weight of 2 new people

= 8X + 151

So,

10X + 15 = 8X + 151

10X - 8X = 151 - 15

2X = 136

X = 68

Now weight of lighter person

= X - 5
= 68 - 5
= 63 kg

Total weight of two people = 151

Weight of second person

= 151 - 63

= 88 kg

Difference between their weights

= 88 - 63

= 25 kg

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