A man travels three fourths (3⁄4) of the total distance of his journey by bus, one sixth (1⁄6) by rickshaw, and the remaining 2 km on foot. What is the total distance travelled by the man (in km)?

Introduction / Context:
This is a fractional distance problem that tests the ability to model a total quantity when parts of it are given as fractions plus a fixed remainder. Such problems are common in aptitude tests and help reinforce the idea that fractions represent parts of a whole and must sum appropriately. The task is to express all segments of the journey in terms of the unknown total distance and then use an equation to solve for that total.

Given Data / Assumptions:

Let the total distance be D km.
Distance by bus = (3 / 4) * D km.
Distance by rickshaw = (1 / 6) * D km.
Distance on foot = 2 km.
All three segments together equal the total distance D.

Concept / Approach:
We use the fact that the sum of the parts equals the whole. In algebraic form, this means bus distance plus rickshaw distance plus walking distance equals D. That gives an equation in D. We simplify the fractional coefficients, combine like terms, and solve for D. Once D is known, we simply match it with the correct option. Carefully adding the fractions (3 / 4 and 1 / 6) is the main arithmetic step.

Step-by-Step Solution:
Step 1: Write the total distance equation. (3 / 4) * D + (1 / 6) * D + 2 = D. Step 2: Combine fractional coefficients of D. (3 / 4) + (1 / 6) = (9 / 12) + (2 / 12) = 11 / 12. So the equation becomes (11 / 12) * D + 2 = D. Step 3: Move the fractional term to the other side. 2 = D - (11 / 12) * D = (1 / 12) * D. Step 4: Solve for D. D = 2 * 12 = 24 km.

Verification / Alternative check:
If D = 24 km, then bus distance is (3 / 4) * 24 = 18 km, rickshaw distance is (1 / 6) * 24 = 4 km, and walking distance is 2 km. Adding them gives 18 + 4 + 2 = 24 km, which matches the assumed total. Thus, the value D = 24 km is consistent with all parts of the journey and satisfies the equation exactly.

Why Other Options Are Wrong:
Option a (12 km) would give 9 km by bus and 2 km by rickshaw, leaving only 1 km for walking, which contradicts the given 2 km. Option b (18 km) and option c (20 km) similarly fail to satisfy the fractions and the leftover walking distance simultaneously. Only 24 km splits correctly into the described fractional parts plus 2 km on foot.

Common Pitfalls:
Common errors include adding the fractions (3 / 4 and 1 / 6) incorrectly or forgetting to express the walking distance separately instead of as another fraction. Some candidates also mistakenly set (3 / 4 + 1 / 6) * D equal to 2 instead of setting the sum plus 2 equal to D. Always start from the fundamental relationship that sum of all parts equals the total and then solve carefully.

Final Answer:
The total distance travelled by the man is 24 km.