A survey shows that 76% of the Indians like Oranges, whereas 38% like both oranges and bananas. What percentage of Indians like Bananas?

1. Break Down the Problem

To find the percentage of Indians who like bananas, we need to use the principle of inclusion-exclusion for the sets of people who like oranges and those who like bananas.

Let:

• $P(O)$: Percentage of people who like oranges = 76%
• $P(O \cap B)$: Percentage of people who like both oranges and bananas = 38%
• $P(B)$: Percentage of people who like bananas (which we want to find)

2. Relevant Concepts

Using the principle of inclusion-exclusion for probabilities, we have: $P(O \cup B) = P(O) + P(B) - P(O \cap B)$ where $P(O \cup B)$ is the percentage of people who like at least one of the fruits (oranges or bananas).

3. Analysis and Detail

From the problem, we know $P(O) = 76\%$ and $P(O \cap B) = 38\%$.

Assuming $P(O \cup B) = 100\%$ (since we are only considering those who like at least one of the fruits): $100\% = 76\% + P(B) - 38\%$ Simplifying this equation will help us find $P(B)$.

4. Verify and Summarize

Combining like terms: $100\% = 76\% + P(B) - 38\%$ $100\% = 38\% + P(B)$ $P(B) = 100\% - 38\%$ $P(B) = 62\%$

Final Answer

The percentage of Indians who like Bananas is $\boxed{62\%}$.