The average weight of 39 Students in a class is 23. Among them Sita is...
Given information:
- Average weight of 39 students = 23
- Sita is the heaviest and Tina is the lightest
- Excluding both of them, the average remains the same
- Ratio of Sita's weight to Tina's weight = 15:8
To find: Tina's weight
Solution:
Let the sum of weights of all students excluding Sita and Tina be x.
So, the sum of weights of all 39 students = x + weight of Sita + weight of Tina
Since the average weight is 23, we can write:
(x + weight of Sita + weight of Tina) / 39 = 23
=> x + weight of Sita + weight of Tina = 897 (eq.1)
Also, we know that excluding Sita and Tina, the average weight remains the same. So,
x / 37 = 23
=> x = 851 (eq.2)
Substituting eq.2 in eq.1, we get:
weight of Sita + weight of Tina = 46
Given, the ratio of weight of Sita to Tina is 15:8.
So, let the weight of Tina be 8x. Then, the weight of Sita will be 15x.
From the above equation, we have:
15x + 8x = 46
=> 23x = 46
=> x = 2
Therefore, Tina's weight = 8x = 16.
Hence, the correct option is B.