The average weight of Shubha, Govinda and Reshma is 65 kg. If the average weight of Shubha and Govinda is 63 kg and the average weight of Govinda and Reshma is 70 kg, what is the weight of Govinda in kilograms?

Introduction / Context:
This question uses averages of small groups to determine the individual weight of one person. You are given averages for three persons together and for two different pairs among them. By translating these averages into equations, you can isolate and find the weight of Govinda.

Given Data / Assumptions:

• Three people are involved: Shubha, Govinda and Reshma, with weights S, G and R in kilograms.
• The average weight of all three is 65 kg.
• The average weight of Shubha and Govinda is 63 kg.
• The average weight of Govinda and Reshma is 70 kg.
• We want the value of Govinda's weight G in kilograms.

Concept / Approach:
We convert each average into a sum equation. From the three person average, we get S + G + R. From each two person average we get S + G and G + R. Using these three equations, we can first find R and then find G, or directly manipulate them to isolate G. This is a common technique in average problems involving three unknowns and three equations.

Step-by-Step Solution:
Step 1: From the three person average, (S + G + R) / 3 = 65, so S + G + R = 195. Step 2: From the average of Shubha and Govinda, (S + G) / 2 = 63, so S + G = 126. Step 3: From the average of Govinda and Reshma, (G + R) / 2 = 70, so G + R = 140. Step 4: Use S + G + R = 195 and S + G = 126 to get R = 195 - 126 = 69. Step 5: Use G + R = 140 and R = 69 to get G = 140 - 69 = 71.

Verification / Alternative check:
Check all three conditions with S, G and R. From S + G = 126 and G = 71, we get S = 55. Now S + G + R = 55 + 71 + 69 = 195, and 195 / 3 = 65, matching the given three person average. Also, G + R = 71 + 69 = 140, and 140 / 2 = 70, matching the two person average. This confirms that Govinda's weight is 71 kg.

Why Other Options Are Wrong:
If Govinda weighed 41, 88 or 46 kilograms, the pair averages 63 and 70 could not both hold at the same time. Substituting any of those values into S + G = 126 or G + R = 140 would lead to contradictions when checking the three person total of 195. Only G = 71 satisfies all three equations simultaneously.

Common Pitfalls:
A frequent mistake is to misinterpret the phrase average of two people and treat 63 or 70 as totals instead of averages. Another issue is mixing up who is in each pair. Always convert averages to totals by multiplying by the number of people, write clear equations and then solve step by step.

Final Answer:
Govinda weighs 71 kilograms.