The average weight of Shivam, Rupesh and Mandar is 45 kg. If the average weight of Shivam and Rupesh is 38 kg and the average weight of Rupesh and Mandar is 50 kg, then find Rupesh's weight (in kg).

Correct option is B

Given:
Average weight of Shivam (S), Rupesh (R), and Mandar (M)} = 45 kg
Average weight of Shivam and Rupesh} = 38 kg
Average weight of Rupesh and Mandar} = 50 kg​​
Concept Used:
​$$\text{Total Sum} = \text{Average} \times \text{Number of observations}$$​​
Solution:
Calculate the total weight of all three persons.
​$$S + R + M = 45 \times 3 = 135 \text{ kg} \dots (i)$$​​
Calculate the total weight of Shivam and Rupesh.
​$$S + R = 38 \times 2 = 76 \text{ kg} \dots (ii)$$​​
Calculate the total weight of Rupesh and Mandar.
​$$R + M = 50 \times 2 = 100 \text{ kg} \dots (iii)$$​​
Add equations (ii) and (iii).
​$$(S + R) + (R + M) = 76 + 100 \\S + 2R + M = 176 \text{ kg}$$​​
Subtract equation (i) from this result to find Rupesh's weight.
(S + 2R + M) - (S + R + M) = 176 - 135
R = 41 kg
So the correct answer is (b)