A car uses 80 litres of diesel to travel 800 km with an 800 cc engine. Assuming that the volume of diesel required varies directly with both the distance travelled and the capacity of the engine, how many litres of diesel are needed to travel 1000 km using a 1200 cc engine?

Introduction / Context:
This question tests direct proportion in a very common aptitude setting involving fuel consumption, distance and engine capacity. The key idea is that the diesel used is directly proportional to both the distance covered and the size of the engine. Once we understand the correct proportional relationship, the numbers become straightforward to handle.

Given Data / Assumptions:

• For an 800 cc engine, 80 litres of diesel are needed to travel 800 km.
• Distance and engine capacity are assumed to affect diesel consumption directly.
• We must find diesel required for 1000 km using a 1200 cc engine.
• Road conditions and driving style are assumed to remain the same in both cases.

Concept / Approach:
When a quantity varies directly with two independent factors, we can model it as proportional to their product. Here, diesel consumption is proportional to distance * engine capacity. Therefore, the ratio of diesel used in two scenarios equals the ratio of distance times capacity in those scenarios. This avoids stepwise mistakes and keeps the calculation transparent.

Step-by-Step Solution:
Let diesel used be D, distance be s and capacity be c. Then D is proportional to s * c. For the first case: D1 = 80 litres, s1 = 800 km, c1 = 800 cc. For the second case: D2 = ?, s2 = 1000 km, c2 = 1200 cc. So D2 / D1 = (s2 * c2) / (s1 * c1). D2 = 80 * (1000 * 1200) / (800 * 800). Simplify: (1000 * 1200) / (800 * 800) = (1000 / 800) * (1200 / 800) = 1.25 * 1.5 = 1.875. Therefore D2 = 80 * 1.875 = 150 litres.

Verification / Alternative check:
Another way is to first find consumption per kilometre for the 800 cc engine, which is 80 / 800 = 0.1 litre per km. Since the capacity rises from 800 cc to 1200 cc, fuel per km scales by 1200 / 800 = 1.5, giving 0.1 * 1.5 = 0.15 litre per km. For 1000 km, diesel required is 0.15 * 1000 = 150 litres, which matches the previous result.

Why Other Options Are Wrong:
140 litres and 120 litres underestimate the effect of the larger engine and the longer distance. 110 litres and 100 litres are even smaller and ignore both proportional increases. None of these values satisfy the direct proportionality with both distance and capacity.

Common Pitfalls:
A common mistake is to scale only by distance (1000 / 800) or only by engine capacity (1200 / 800) instead of combining both factors. Another frequent error is to treat consumption per kilometre as fixed even when engine capacity changes. Reading the phrase “varies directly as the capacity of the engine” carefully prevents these misunderstandings.

Final Answer:
The volume of diesel required is 150 litres.