Tapas, Avi and Rishi share a cake. Tapas eats 1/2 of the cake and Rishi eats 1/3 of the cake. Avi eats the remaining part. What fraction of the cake does Avi eat?

Introduction / Context:
This is a simple fraction and complement problem. It tests comfort with adding fractions and determining the remaining part as a fraction of the whole. Such questions appear in early quantitative aptitude and school level mathematics.

Given Data / Assumptions:

• The total cake represents one whole unit.
• Tapas eats 1/2 of the cake.
• Rishi eats 1/3 of the cake.
• Avi eats whatever is left.

Concept / Approach:
The total fraction eaten by Tapas and Rishi together is the sum of their shares. The remaining fraction for Avi is obtained by subtracting that sum from 1 (the whole cake). The process involves adding and subtracting fractions with different denominators.

Step-by-Step Solution:
Tapas' share = 1/2.Rishi's share = 1/3.Sum of their shares = 1/2 + 1/3.Find common denominator 6: 1/2 = 3/6 and 1/3 = 2/6.So 1/2 + 1/3 = 3/6 + 2/6 = 5/6.Total cake = 1, so Avi's share = 1 - 5/6 = 1/6.

Verification / Alternative check:
We can imagine cutting the cake into 6 equal pieces. Tapas would eat 3 pieces, Rishi would eat 2 pieces, and that accounts for 5 pieces. The remaining 1 piece out of 6 belongs to Avi, confirming the fraction 1/6.

Why Other Options Are Wrong:
3/5, 2/6 and 3/6 do not represent the remaining fraction correctly. In particular, 2/6 and 3/6 correspond to 1/3 and 1/2, which have already been assigned to Rishi and Tapas. The total shares would exceed the whole if any of these were given to Avi.

Common Pitfalls:
A typical mistake is to divide the remaining fraction 1/6 further or miscalculate the addition of fractions by adding numerators and denominators separately. Always work with a common denominator and then add or subtract numerators as appropriate.

Final Answer:
Avi's share of the cake is 1/6.