Three friends have dinner at a restaurant. When the bill arrives, Akshitha pays two thirds as much as Veena pays, and Veena pays half as much as Lasya pays. What fraction of the total bill is paid by Veena?

Introduction / Context:
This is a ratio and fraction based aptitude question framed around sharing a restaurant bill. The goal is to use the given relationships between individual payments to express each person's contribution as a fraction of the total amount and then determine Veena's share as a single fraction.

Given Data / Assumptions:

• Three friends are Akshitha, Veena and Lasya.
• Akshitha pays two thirds as much as Veena pays.
• Veena pays half as much as Lasya pays.
• The total bill is the sum of the amounts paid by all three friends.
• We must find the fraction of the total bill paid by Veena.

Concept / Approach:
We translate each comparative statement into an algebraic relation using variables. Then we express all payments in terms of a single base quantity, usually the largest amount. After that, we form the total bill and compute the fraction that corresponds to Veena's share. This type of structured algebra makes it easy to simplify the fraction correctly.

Step-by-Step Solution:
Step 1: Let Lasya's payment be L rupees. Step 2: Veena pays half as much as Lasya, so Veena's payment V = L / 2. Step 3: Akshitha pays two thirds as much as Veena, so Akshitha's payment A = (2 / 3) * V. Step 4: Substitute V = L / 2 into A: A = (2 / 3) * (L / 2) = L / 3. Step 5: Now express the total bill T as T = A + V + L. Step 6: Substitute A and V in terms of L: T = L / 3 + L / 2 + L. Step 7: Use a common denominator of 6: L / 3 = 2L / 6, L / 2 = 3L / 6, and L = 6L / 6. Step 8: So T = 2L / 6 + 3L / 6 + 6L / 6 = 11L / 6. Step 9: Veena's share V is L / 2, but we want this as a fraction of T = 11L / 6. Step 10: Fraction paid by Veena = V / T = (L / 2) / (11L / 6). Step 11: Simplify this: (L / 2) * (6 / 11L) = (6L) / (22L) = 6 / 22 = 3 / 11.

Verification / Alternative check:
We can choose a convenient value for L to verify. Let Lasya pay Rs. 22. Then Veena pays half of that, which is Rs. 11. Akshitha pays two thirds of Veena's amount, which is 2 / 3 * 11 ≈ 7.33. The total bill is 22 + 11 + 7.33 = 40.33. The fraction Veena pays is 11 / 40.33, which is very close to 0.2727. The fraction 3 / 11 is approximately 0.2727 as well, so the theoretical fraction matches this numerical check when we ignore rounding of Akshitha's share in rupees. In exact fractional form, the algebra gives a precise answer of 3 / 11.

Why Other Options Are Wrong:
11 / 3 and 13 / 4 are greater than 1, so they cannot represent a fraction of a total bill.
2 / 13 is much smaller than 3 / 11 and does not match the algebraic calculation. Therefore it is also incorrect.

Common Pitfalls:
Learners may misread phrases like "two thirds as much as" and mistakenly treat them as "two thirds of the remaining bill". Another mistake is to forget to compute the fraction with respect to the total bill, instead of just comparing with one person's contribution. Always define variables clearly and form the ratio of the required amount to the total sum.

Final Answer:
Veena pays 3/11 of the total bill.